Quote:
Originally Posted by
holymadness 
When the temperature of the air is >37°, however, it ceases to cool the body.
At that temp, it ceases to cool the body through convection, because you can't cool anything below the ambient temp that way, and the body temp is usually around 37°. However, by the mechanism you propose, which only works if you are actually sweating, btw, there's no reason why high ambient temp would cause you to stop losing heat through evaporation of sweat.
Change in free energy (∆G) = ∆H - T∆S. If free energy decreases due to a process, that process will spontaneously occur. H is heat, S is entropy. When sweat evaporates it requires energy to do so (to overcome intermolecular forces); however, this energy is offset by the second term in the equation, which is large due to the increase in entropy (gas vs liquid). As temperature increases the entropic contribution becomes more significant and gasses are favored. ∆G changes, but ∆H does not. The process still requires heat, which has to come from somewhere.
If you are arguing that the requisite heat comes from the atmosphere rather than from the water droplet itself, my answer is that it still doesn't matter, because the change in heat will still have a cooling effect, directly or indirectly, versus what you would feel without sweat.
