“How do soldiers cope in intense heat when they are deployed abroad and have to do stuff and carry their full kit?”
As with the other answers, I can say that we dealt with it as best as possible because there were no other options.
As part of a Medevac crew, we had several different techniques. We were unable to benefit from the microclimate kits installed in the helicopters (disconnecting and reconnecting the hoses that went to the vests associated with this system was impractical as we were constantly getting in and out of the helicopters), so we kept bottles of water in a freezer in our operations area. These we grabbed on the way out to the birds, and it was not uncommon for a large plastic bottle of ice to become lukewarm by the time we were on our final approach on some missions.
We progressed to carrying coolers full of these same frozen bottles, and these usually had five or six Gatorades as well. With this, the challenge was making sure that the drinks were still cold, as we would stock them in the morning during our runup and typically forget about them if we had no missions that day.
However, my own personal solution was discovered accidentally. I was reading about glassworkers and the article highlighted how they kept chilled tomato juice handy. Something about the sodium being more beneficial clicked. In the summer, you could tell how many missions the crew went on by counting the distinct salt rings on their flight suits; on more than once occasion, my own clothes had become stiff and coarse with salt by the end of the day.
Since we had no tomato juice handy, I looked at the next best thing: the pallets of canned V8 that sat unused in the corner of a common area (apparently, most folks in the Army will not touch the stuff unless there is vodka handy).
Once they were dusted off, cleaned, and refrigerated, these cans became my elixir of comfort. The high sodium levels in V8 — potentially problematic in non-deployed life — effectively replaced much of the salt that was leached out during perspiration, and actually tasted much better than the funky-tasting bottled water procured in bulk from local distributors.
Upon returning home, it took a while for me to be once again enjoy V8 in clear containers, not because of the taste, but because the visual reminder of some of. To this day, though, V8 has been my go-to drink when working outdoors in the Georgia/Alabama heat.