Evolution of the human brain

[ChrisV]

I've been reading a book recently ("Our Kind", Marvin Harris) and it discussed hypotheses of the evolution of the human brain, in particular the large increase in size observed in erectus. The book advanced the theory that the increase in size was to provide backup neurons for when neurons were failing due to heat stress and exhaustion. While humans are not fast runners, we are able to run continuously for longer than virtually all species. This enables fit people to "run down" game such as deer, simply chasing them until they collapse from exhaustion. This method of hunting is still practiced by some peoples today, and could have been a selective pressure in human evolution. The book advances the idea that increasing the number of neurons in the brain enabled humans to handle heat exhaustion.

Has anyone heard this hypothesis before, and is it still thought plausible today? The book was published in 1989 so it is likely to be out of date.