There is one thing that humans have done for which lack of fur would be an advantage: using fire, particularly in open/windy areas. That is, an incident which might cause a minor burn to a human could easily light a neandewrthal or some other hominid up like a torch and fry him. Humans were designed to use fire, that had nothing to do with evolution or any other kind of junk science.
I agree that’s another advantage of going furless but unlikely that threat was pervasive enough to be a factor in natural selection.