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OK, it's complicated :-) I'm really over-simplifying a lot, but essentially the brain has constant activity going on, and "thinking" - in which I include everything from ongoing involuntary nervous system activity up to playing chess - is just changes in the patterns of activity. It's the difference between being asleep or unconscious, and brain dead.
But of course there's an easier way to see that thinking doesn't use much energy, by starting from the other end. What happens when you ride a bike, or do any exercise where you're burning significantly more calories that when you're at rest? You breathe deeper to take in more oxygen to burn the calories, your heart speeds up to transport more oxygen &c around the body, if it's warm you sweat a bit because of the extra heat generated by the calories burning. So does any of this happen when you're thinking hard about something?
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