Sweating can cool you down even if the air temperature is higher than your body temperature, since the evaporation of sweat consumes some of your body heat.
The relevant metric is the so called “Wet Bulb Temperature” which is the temperature that a wet thermometer will measure in wind, and takes evaporative cooling into account.
Wet bulb Temperature depends on both humidity and temperature, wheras as standard “dry bulb” temperature dependends only on, well, temperature.
A wet bulb temp of around 35°C or higher is the point where the conditions are no longer survivable for more than a few hours, regardless of shade or hydration.
You sweat. This liquid on your skin now vaporize, this effect needs energy and cools it’s surrounding, leading to you cooling down.
That’s also the reason why people think humid heat is worse than dry heat. If the air is already full with liquid your sweat won’t vaporize as easily (or not at all) which now doesn’t cool your body down.
If the air is dry, you sweat out the excess heat- water evaporates off your skin, flinging the hottest molecules away and keeping the cooler ones. If it’s too humid, you can’t sweat effectively, so you can’t cool down. This is why high wet-bulb temperatures are a cause for concern- without active cooling (Air conditioning, refrigeration) even mild temperatures will kill you if there’s enough humidity.
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