IIRC, tools have been dated back to 2+Mya, and braincases were up to 1 liter around 1 Mya, by which point tool use was prevalent, but fire use was tentative. By the time fire use was prevalent, I don't think brain size has changed more than 10%. So the big expansion of brain size was in the time of early tool use, not fire use.
Many people have pet theories as to what drove human evolution, but I doubt it was any single cultural advancement. Language is an example of one that many people also push as being "the" cause of human evolution. I suspect they are all important, but there was no "the" cause, although specific genetic events might eventually be identified as being quite significant. The problem with tools, fire, language, etc, is that quite a few different species all had them, but only we remain. So at best, you could try to claim we had them in better degree than the others. |
