Eric Nord voted up this answer.
The switch to persistence hunting (as in Lee Thé
's answer) meant a re-engineering of the human heat-management system.
To run an animal to death in the mid-day African sun, requires the hunter to have the biological equivalent of high-power air-conditioning. A top athlete is able to dump 750W.
Instead of adaptations to keep us warm, we needed adaptations to dump heat. Sweating means being able to operate at full capacity in environments that are warmer than body temperature.
The chimp / bonobo fur had to go. If we kept it, we'd cook just like the poor actors on the set of 2001.
And as any teenage kid with a gaming-PC will tell you. If you upgrade your cooling system, you can safely overclock your processor. A better cooling strategy meant we could increase brain size.
The explosion in human cognition could have been a direct consequence of this adaptation. We became smart because chasing Wildebeests was a sweaty business.See question on Quora