Humans have very little hair, compared to our close primate relatives. This obviously raises questions about why, when, and how humans evolved to be hairless. However, hair doesn't fossilise because it isn't made of bone. The resulting lack of information makes it difficult to come up with a decent answer for any of these questions.
Thus scientists have to rely on other avenues for investigation; like studying the evolution of lice. The body louse and head louse are different subspecies in humans, likely splitting when their respective habitats were isolated as humans became hairless. Another approach is to explore the implications of losing hair to try and find out when it may have become feasible. Such research has helped narrow down when humans evolved to be hairless by ruling out certain periods of time; when losing hair would have harmed humans.
Hairless goosebumps
The main function of hair amongst our close relatives is thermoregulation. The obvious benefit being that it traps heat in, keeping them warm. Like a fuzzy, huggable jacket. However, under certain circumstances, it can also keep you cool as well. It prevents animals absorbing as much heat from the surrounding environment. Their fur absorbs and dissipates some of the heat, rather than having it all be exposed directly to the skin.
Our ancestors lived in Africa, where the warmth of a full body of hair wouldn't have been especially useful. In fact, it may have been outright harmful. Chimps only tend to be active for around 20% of the day and it's hypothesised they can't move about more often because they'll overheat due to their thick fur. At the same time, they (and likely our ancestors) couldn't have become hairless because that same heat that keeps them immobile would be exposed directly to their skin; causing yet more problems. Our ancestors would have been walking a rather furry tightrope.
Enter the another major change (or rather, modification) that happened over the course of human evolution: walking upright.
If you imagine looking at a bipedal and quadrupedal ape from above (where the sun lives) you can see a lot less of the bipedal one. Their "footprint" is reduced. Additionally, being bipedal tends to make you taller, bringing you up in the atmosphere; up where the air is clear. And cooler. Both of these are rather small changes, but calculations have shown they might have been enough to help our ancestors stay cool despite their natural, furry sunblock.
Lucy the Naked Ape?
However, there is the other side to that tightrope. Hair does keep you warm, after all. When you're out living on the Savannah heat might not seem like something you want a lot of. But things change at night when the temperature plunges. This is particularly problematic at high latitudes, where things get even colder. This is where our more ape-like ancestor, Australopithecus, lived.
The obvious solution to this dilemma would be to move down the hill a bit. However, during the day these lower, more open environments get even hotter. That hairy tightrope becomes even thinner and harder to balance on; with our ancestors being trapped between a rock and a hot place. These problems would have been exacerbated by the fact Australopithecus bipedalism was a bit less efficient than ours. The result being that even if they lost all their hair they probably couldn't have survived on the open plains.
Thus, Lucy and her kin were stuck up the hill with their fur; unable to travel down. However, it isn't an all-or-nothing scenario. Minor improvements to bipedalism or their fur would allow them to head a little bit further down the hill. Exploit a slightly new area. This would have obvious benefits, allowing them to access new food sources their less bipedal friends couldn't.
These gradual, incremental benefits could easily drive gradual, incremental evolution. Sure enough; over time we see our ancestors getting better at bipedalism and moving down towards the coast. Likely they were losing their hair as well. So whilst we still can't pinpoint exactly when it happened, it must have been after Australopithecus.
We're gradually shaving away this mystery (ha).
Summary
Hair keeps you cool during the night and warm during the day. This would have meant becoming hairless would require extra adaptions, which didn't emerge until later in our lineage. Thus hairlessness likely didn't either.
References
Dávid-Barrett, T. and Dunbar, R.I., 2016. Bipedality and hair loss in human evolution revisited: The impact of altitude and activity scheduling. Journal of human evolution, 94, pp.72-82.
Rantala, M. J. (2007). Evolution of nakedness in Homo sapiens. Journal of Zoology, 273(1), 1-7.
Ruxton, G. D., & Wilkinson, D. M. (2011). Avoidance of overheating and selection for both hair loss and bipedality in hominins. Proceedings of the National Academy of Sciences, 108(52), 20965-20969.
Wheeler, P.E., 1984. The evolution of bipedality and loss of functional body hair in hominids. Journal of Human Evolution, 13(1), pp.91-98.
