We’ve talked about why brains got bigger with time, but the Neanderthals stood out as an outlier and needed further research and explanation. We’ve also shown the benefits of larger heads in sports, but we never really answered the question: how did they get this way?
Neanderthals heads were bigger. “Neanderthal populations in Europe endured many environmental changes, including large shifts in climate between glacial and interglacial conditions, while living in a habitat that was colder overall than settings where most other hominin species lived. Some of the environmental shifts they endured involved rapid swings between cold and warm climate.”
Other ancient men’s heads were smaller, and were hairier. If the brain is a heat source, these other ancient men need additional heat to survive.
Races of people in cold environments have larger heads [and smaller eyes].
People in warmer climates typically have smaller heads. And we’ve theorized about the strengths and weaknesses of each of these qualities. 
If the brain is a heat source, that would explain all of these cases. Colder environments need more heat, and hot environments need less. Further, over thousands of years, the climate would naturally select some of the distinguishing qualities of these races.
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