Why do we grow so much hair on our heads compared to our bodies?
Wheeler (1992; and previous) discusses the evolutionary loss of "non-functional" hair in hominids from the perspective of water balance. 

Wheeler's hypothesis is that naked, bipedal hominids could have tolerated higher ambient temperatures as well as elevated metabolic heat production. Naked skin would confer higher levels of evaporative cooling, but would have entailed more water loss. 

Wheeler argues that bipedalism necessarily would have preceded loss of hair, which seems to agree with Carrier's (1984) hypothesis that early hominids were distinguished not by large brains but by upright, bipedal postures with striding gaits. Humans are unique among similarly sized mammals in their capacity for endurance running.