How do we cool exactly as sweat evaporates from our skins? We all know that when our sweat evaporates to the air we feel colder, but since this process is a latent heat transfer our body temperature will not change, then if our body temperature is constant how do we cool down?
 A: Evaporation occurs at all temperature and it that way it is unlike boiling.
Consider your body as the system with some water (sweat) on the skin.
On average the faster molecules in the sweat "evaporate" lowering the average kinetic energy of the molecules in the sweat and so the temperature of the sweat decreases.
As the sweat is cooler than the skin heat is transferred from the skin to the sweat.
A: To expand slightly upon Farcher's answer:
At any air temperature at which it is a liquid, water molecules will be striving to evaporate from that body of liquid at a rate which depends on the ambient temperature (higher means faster) and on the relative humidity (i.e., moisture content) of the air at that temperature (lower humidity means faster). In so doing, they will carry away the latent heat of vaporization from your body and deliver it to the surrounding air.
So for example if your skin and the air surrounding it is at 75F and low relative humidity (as in a desert) and it is covered with a film of water (as sweat), then your skin will cool down by evaporation.
The cooling effect (delta T) you can achieve by this method is thermodynamically limited to the dew point temperature of the air, at which your skin is so cold that the relative humidity of the air at that cool temperature is 100%, and net evaporation ceases.
In practical terms, you can never achieve that number, and the usual figure for delta T assuming desert conditions (<10% relative humidity) is about 20F.
