My first suggestion for working in extreme heat is to weigh carefully the necessity of doing so. Can the project wait? Are you acclimated to working in the heat or will you be putting yourself at risk by doing so? Remember that taking a chance and getting injured means you'll be taking up emergency resources and potentially even putting the first responders at risk as well. If you are not used to the heat and haven't built up a resistance over time my best advice is to find somewhere chilly and settle in until the heat wave passes. But, if you don't like that advice let's get into what you can do to stay reasonably safe.
1. You've got to stay hydrated. I usually don't carry a camera bag or backpack with me when I go out shooting during most days. The exception is when I'm working in the heat. Anything over 95° makes me more cautious. If I'm being cautious I bring a small shoulder bag or backpack and I bring along two 16 ounce bottles of water. If I'm being indulgent I fill one of the bottles with ice from the freezer and top it off with water. It'll stay cool for a while. I start drinking before I start feeling thirsty and you should too.
Figure on downing at least eight ounces per hour. Minimum. If the heat and humidity combined yields a heat "index" (or "feels like") of 105 or higher then double that. If you are bigger than I am add more to the total. Your goal should be draining your last supplies just about the time you make it back to your car or your air conditioned destination.
I also keep a 32 ounce bottle of water in my car, right next to my swim gear. If I'm feeling a bit overheated when I make it back I will soak my shirt and hat (but not my straw hat!) with some of the water and couple that cooling power and the evaporative cooling with that of my car's air conditioning. Even standing in the shade, soaking wet, with a slight breeze will go a long way toward lowering my skin temperature and helping to lower my core temperature. When we worked in the vineyards last August for the Texas Wine project I tried to keep my shirt and hat damp and cooler as I worked. It sure helps.
2. When walking through city streets you'll usually find one side of the street is in shade and the other in direct sun. Obviously you want to walk on the shaded side which generally means avoiding being at a location during a time when the sun is directly overhead because.....no shade. For downtown Austin this means the best shooting times are from sun up till about 11:00 a.m. and then again from 2:30 p.m. till sunset.
3. Think about devising ongoing shade for your black bodied cameras and their black bodied lenses. I love shooting photographs with a Leica SL but there's a design flaw that comes to the fore when you get out in super hot, direct sun. The body is made of black metal and it acts as a heat magnet. If you leave it out in the sun it can get hot enough to burn your hands and, even worse, the heat affects the electronic noise of the system which makes your images noisier and peppered with various visual artifacts. There are a couple solutions. I have actually thought of painting one of the two SL cameras white. I'd do this to reflect the sunlight and reduce the heat absorption. It's a radical idea. But a more practical idea would be to bring along a small shoulder bag that's made in a very light color and keeping the camera and lens in the bag until such a time as you need it. Sure, it's not a quick approach to street photography but the upside is no burned hands and no images ruined by noise caused by excessive heat.
With a camera that's well sealed against moisture and dust intrusion you might even consider wetting down the camera bag to take advantage once again of evaporative cooling. Works best on canvas bags. The same bag that carries your water supply.
4. Hopefully you will sweat as you walk out on the streets in the heat and humidity. That consistent sweat goes a long way towards keeping you alive. But it's a bit problematic when it comes to camera handling since sweaty hands are slippery hands. I carry a small, white terry cloth rag with me, stuffed into the side of the camera bag or in a back pocket. I use it to wipe the sweat off my hands before handing the camera. In a pinch I can wet the rag and use it around my neck to cool off. Sweating though is good but it's also a sign that you need to keep drinking water. If you stop sweating on a hot day you are already in trouble and need to seek shelter and help as quickly as possible.
5. It's hard to find sunglasses that are not polarized but it may be well worth the effort for two reasons. First of all I'm sure you've noticed that everything, every sky, every lake or pond looks better and more exciting through polarized sunglasses so if that's your point of visual reference you'll be disappointed when the images you photograph don't match the enhanced sizzle that you see through your polarized sunglasses. A pair of sunglasses without the polarization will still do a good job blocking UV and IR energy from hitting your eyes and bringing along the prospect of long term, progressive damage, and you'll be able to see your intended photo subject in a realistic way. And deal with it accordingly.
But the second reason is that with some EVF viewfinders and LCD rear screens you might lose the view altogether. I noticed recently that when used the Leica CL in the landscape mode I was able to see the rear screen with no issues; even with my polarized, prescription sunglasses on but when I turned the camera to portrait mode the viewfinder blacked out. The polarizing screen and the grid screen on the camera cancelled each other out. In that case I pulled off my sunglasses and composed the now revealed image again but it delayed the shot and also gave me something else to keep my hands overly filled.
I fished around in the center console of the car later that afternoon and unearthed a pair of Ray-Ban sunglasses that were not polarized and found that, while the sky didn't look nearly as exciting, the screens of my camera didn't black out when I turned them by 90 degrees. If you are into pre-visualization the polarizing nature of some sunglasses isn't doing you any artistic favors. Yes for driving and boating but, sadly, no for working with cameras of various vintages. ( I first saw this effect, the blacking out of a screen, with the optical finder of the Mamiya 6. I think owning several of those cameras is what drove me to buy the Ray-Bans in the first place.
6. Dress for it. Going out in a "Summer" wool suit with a Nicole Miller necktie is very much contraindicated. You'll roast and probably spend a fortune getting the suit cleaned back up. The reaction from people unaccustomed to severe heat is usually to wear a pair of shorts and a tank top or t-shirt. Maybe a pair of sandals. A baseball hat (uniquely American?). And that's okay when you are dealing with lower temperatures and lower UV energy ranges (thinking 70-95°) but it's the super strong rays of the sun that drive up the heat so you need two things: clothes that breathe and wick away sweat for better cooling, but also clothes that cover as much skin as possible. You really don't want to sport a bad sunburn in conjunction with uncomfortably high ambient temperatures. It's discomfort squared.
I want a long-sleeved shirt made from a very thin fabric that invites breezes and does a good job wicking away sweat --- again, thinking about the evaporative cooling effect. But I also want a shirt that is rated at 30 or 40 or more SPF or UPF to keep my skin from burning. A shirt with vents is also great. And do yourself a favor --- we know artists are supposed to go around dressed in black --- but just for this special situation consider light colors. White, near white, almost white, sorta white and, in a pinch a very light beige. You want the most reflection of heat and radiation you can get commensurate with providing enough protection. Sure, you won't look as cool without the black turtleneck but you'll actually be cool(er).
Same with pants. Unless you want to play "Where's Waldo?" down the road with various skin cancer tumors you'll want to cover those "I mostly work indoors on a computer" legs. There's a clothing maker called Kuhl that makes great long pants with vents hither and yon and they are cool to wear. My favorites are the REI Sahara pants which feature thin fabric, stated protection and the ability to zip off the legs of the trousers, below the knees. Which in most situations (other than extreme heat) is tres nerdy. I wear them long when in the sun for all the reasons we've already covered but I sometime zip off the lower legs when I'm somewhere with cool air so they can help me lower my core temperature. I hide behind my sunglasses while doing so.
That covers the middle but don't forget the top and the bottom of the package. You know you need a hat. But it's not the time for a beaver pelt, Stetson, Open Road hat. They don't breathe at all and they insulate your head like crazy. You'll fry your brains! You need a good bucket hat or, God forfend, something like a wide brim Tilley-esque hat. Something that casts shade on your face and especially the tops of your ears. But also something with some flow through ventilation near the top.
I have more hats than I have cameras and that's saying something. But a good hat can help keep you cool, will protect your skin and has the added benefit of acting as a lens hood for your own optical system; your eyes. If I'm planning be outside for a long period of time I grab for the hat with the biggest brim in the stack. The bigger the brim the more available shade for your neck and shoulders, and it's just basic science that the less radiant heat you soak up the better you'll feel and the longer you can go. This Summer's favorite is a bucket hat I bought from REI. It's their store brand. I like it because it's very light weight, has a wide enough brim, and the brim is flexible enough to give when I press a camera up to my eye. And about a third the price of a Tilley chapeau. The Billingham bag of hats....
At the other end it seems to make sense to wear sandals but you would be wrong. On a nasty hot day you have too much danger of getting parts of those naked feet burnt to blisters by the sun. But another consideration is the surfaces you'll be walking across. If you are spending a lot of time on pavement or, even worse, asphalt, you'll find that the ground beneath your feet has done an exemplary job of soaking up heat. Especially black top. A sturdy pair of hiking shoes or mid-weight hiking boots is actually the optimum tool for the job. The thicker soles do a better job of insulating you from the pavement. The thicker soles slow the heat transfer way down. Long term your feet will get less hot even though that seems counter-intuitive. Plus good, enclosed shoes are better for stomping on scorpions or accidentally stepping on broken glass or nails.
7. With extreme heat comes extreme UV radiation so it almost goes without saying that you should cover any exposed skin with a good sunscreen. Even the parts of your face that exist under your bucket hat. Remember, there is such a thing as reflection. You might even consider using a reflective umbrella. Create our own, wider shade...
8. Plan your activities with an eye to accessing cooling interior spaces. If you start to get too hot take refuge in a hotel lobby, a library, a museum or a coffee shop. On the days where my planning is off and my immediate feeling is that I've bitten off more than I can chew (heat-wise) I make a straight line to the W Hotel. They have a cool lobby and it's rare anyone is there. I mean, in the lobby. In the winter I sometimes go in for a ridiculously expensive coffee but I don't mind the price since I consider that I'm offsetting my taking advantage of their largess in the Summer months. Twenty or thirty minutes of cooling, along with a good act of re-hydration, can literally be a lifesaver. And if you feel as though you can't go on you've got a nice place to wait for a car share ride back to your vehicle.
I've got downtown planned out so I'm rarely more than 800 yards from some refuge from the heat. You should plan for that too.
9. Park your car in the shade. Put up the windshield sunscreen. If you can't find a shady spot or there are no shady spots then go ahead, piss away the money, and park in a garage. You'll be much happier if you come back to a warm car rather than a raging inferno of a car interior. And your car will thank you for at least temporarily reducing the heat stress. If it's hot for more than a week be sure to monitor your car's battery. Heat is one of the biggest causes of premature battery death. And being stuck somewhere when the temperatures are hitting the danger zone is absolutely no fun.
10. This is my final number and a catchall for everything else.
Don't bring along a lot of black metal. Like that enormous, black metal Benro tripod I own. The metal soaks up heat like a sponge and transfers it efficiently back to your waiting hands. Ditto black light stands, etc. Leave all that stuff at home. You'll quickly get too tired to carry it as you spend more time in the inclement heat. It has a way of draining energy from even the most disciplined workers. Same with black hats, black backpacks and the like.
Walk slower. You don't have to walk in slow motion but if you usually walk at a brisk pace tone it down about bit because every added bit of speed takes its toll on the body. Find a pace that's comfortable instead of competitive. It might take a bit longer to get anywhere but with street photography and what not isn't the journey the important thing? I walk a about sixteen minutes per mile in comfortable weather. I measured last Sunday when it was near 110° and my pace was about 25 minutes per mile. For about a mile. Before I realized that walking in that dangerous stew of heat and humidity might kill me.
Always tempting somewhere along the route to stop in some where for a cold, frosty beer. Normally I'd be right there with you but in extreme heat that brewski will dehydrate you at the speed of light. And the affects of the alcohol will be enhanced. But if we're talking extreme conditions it's the exact time that you need all your wits about you because the heat saps your attention and your reasoning skills.
Finally, if you start to feel bad get into someplace out of the heat and get help right away. Heat kills far, far more people every year than even the worst cold. Quick action saves lives. And, if you want to be a good guy, be sure to keep an eye on all those people around you, watching for signs of heat exhaustion and other distress. Your quick action might save, or at least improve, some stranger's life.
Also.....finally, finally, don't take your dogs out in this. The pavement will torture their paws and they don't shed heat nearly as efficiently as humans. Taking Rover out in an urban heat jungle is just cruel.
Bring an extra battery for the camera. The heat affects them too. Keep your cameras cool enough so the lubricants in the lenses don't vaporize and coat the internal elements. That'll save you money.
Be careful out there. And, if this is a wildly unusual circumstance for you then you have my empathy and my sympathy. Go slow and stay in the shade. And have that water bottle handy.
all done for now.