To make a further contribution to what is clearly becoming a heated discussion - the heat loss from your evaporating sweat is cooling you down and therefore aiding your survival. But the process has its limits. As the temperature rises (in my experience, somewhere above 104F or so in a low humidity situation) you had better curtail activity and stop generating heat.

We probably should distinguish between the effects of heat and those of dehydration, which can be insidiously fatal at surprisingly low temperatures.