Your brain is just one extremely power hungry processor. If it's tasked with any slightly tougher calculations, such as during a game of chess, you'll be burning hundreds of calories an hour. This also has the side effect that most professional chess players aren't fat.
It also helps to further cement the idea that there is a link between being fat and being dumb. If you don't train your brain, you'll burn less calories and the odds of ending up fat increases.