I grew up in Texas on a farm, so we had heat and humidity. Our home had a window refrigerated A/C in one room. We had a whole-house fan that exhausted into the attic. We ran that at night. Basically, we just sweated.

My wife and I camp at Burning Man every year, and it hits the hundreds on occasion and nineties most days, but there's no humidity. We have a shade tarp with flaps to the ground on 2 sides. This shades us from exposure to the sun without blocking any air flow. This means we stay ambient temperature, but not higher. I drink copious amounts of water and stay out of the sun during the heat of the day. We have water misters (those spray bottles for misting plants or your clothes if you iron by hand), and we spray each other to cool off occasionally. We bring a plastic tub and soak our feet in it - it's surprising how cooling that is, just sticking your feet in a tub of ambient temp water. Basically, we just sweat.

The good thing about the location at Burning Man is that it's high desert so it gets cool at night.

Drinking a lot of plain water may bring on hyponatremia, so at Burning Man we watch our electrolyte intakes to make sure we're getting enough. We drink juices and eat salty food.

Many people run around naked, but I have vitiligo, so I keep my skin covered in cotton and breathable fabrics that soak up sweat and evaporate it. I wear a hat any time I'm out in the sun instead of a cap. The hat has a reasonably broad brim and a stampede string so it doesn't blow off.

If you can conserve sweat, you can do fairly well. Spraying a mist on the skin can be shockingly cold and take your breath away if you do it right. There's no way to stay cool if you have no power, so shade that doesn't block breezes and trap heat, keeping hydrated (with electrolytes), and managing my activities is the way I handle it.