Vulcan:
The body is only cooled in sweating when the sweat evaporates.
Initially the skin is covered in sweat which is not seen (Insensible sweat) and when this evaporates......the body temperature falls.
The next stage is "perceptive sweat"...you can see it and feel it and when this evaporates, the body is cooled.
NOW......when you sweat to such an extent that it "drips off you" it doesn't have time to evaporate and hence has no effect on body cooling.
So you see, there is sweat and there is sweat.....;-)