This is actually incorrect, the temperature of the burned gases is directly related to how hot they are before they start burning. A hotter intake charge will produce hotter end temps during/after combustion; this is why one of the best ways to reduce detonation is to cool the intake charge because the burn temps are reduced to where the unburned gases in the chamber won't combust on their own before the flame front moves through them. The reason colder intakes make more power is simply because colder=denser and you get more fuel/air in each of the cylinders in each intake stroke.
