Surface area vs. volume
I always thought that as as sphere got larger, the surface area per unit volume decreased.
As I see it, it comes down to heat dissipation - a larger skull has less surface area relative to the volume of brain matter within it, which means in a hot environment there would come a point where the brain couldn't be cooled adequately, and this would form a limiting factor.
If the air is cooler then more heat can be dissipated as the thermal gradient vs the head is higher, which means the upper volume limit changes and larger brains/heads become viable.
Beyond a certain point I would guess that cooling isn't as much of a problem as retaining heat, and this could have other impacts eg. need for more hair - plus it could drive even larger growth just to keep the volume/area relationship low.
This of course is what engineering suggests as the simple & obvious explanation - differing environmental challenges leading to a requirement for a larger brain doesn't seem quite so elegant, but thermodynamics probably isn't a strong point for biologists.
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