Sweating is not really a great way to cool off. It only works well under a breeze.
One idea I came across in a graduate school evolution class was that the lack of body hair was related to sweating and developed due to persistence hunting. Running, as is required for persistence hunting, would provide the necessary breeze.
The time for this was placed with development of the earliest
Homo species.
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.