Lick your hand, and then blow on it. Your saliva should be body temperature, roughly 98-degrees F. Blowing on it feels cool because when a liquid evaporates, the conversion from liquid to a vapor absorbs a lot of heat.
When your sweat evaporates into dry air, it cools you a bit. You may still feel hot, but you would feel hotter if the air cannot absorb any more moisture because it already is holding as much humidity as it can.
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