You generally get better power from cool AIR. Its denser, so each engine stroke has more O2 to react with. The fuel, however is different. I think, ( im not certain), but I think the fuel will react better if it is warmer. Generally speaking, heat is a catalyst in most chemical reactions.
Nitro methane is a long carbon chain molecule with an oxygen on the end of it. The purpose of the nitro meth is to use that loosely attached O2 . Its the same principal as nitrous oxide. Essentially, you are simpley adding more O2. Thats the best I can remember of chemistry that I had 25 years ago. I'm no expert.