Nitromethane is an interesting energy source, but there is a lot of nuance in what it does and why.

It can cool the inside of the engine - somewhat true, since it takes roughly twice as much heat energy to vaporize nitro than methanol. On the other hand it in high percentages can send the piston right out the exhaust in just a few seconds after an engine goes lean. This then requires a new piston, sleeve and head.

Low BTU output - true compared to methanol.

Makes it's own oxygen - somewhat, as it does have oxygen in the molecule. But it still needs oxygen from the air to burn. The big difference is the air/fuel ratio. Methanol needs about 5 to 6 lbs of air for each lb of fuel to completely burn, while nitromethane only need 1.7 lbs of air for each lb. This is known as the stoichiometric ratio, which is about 14.7 for gasoline.

So why does it make so much power? It is mostly due to the amount of mass of heated gases you get on top of the piston that does the work. Since you can run about three times as much fuel through an engine (comparing 65% to 15% nitro fuel), the power goes up considerably. My racing .40's used about 3 oz of fuel a minute on 65%. They also used up a glow plug each flight. And you had to adjust the load and the head clearance based on the density altitude, temperature, and humidity. High pressure days at low altitudes at about 70 degrees and 30% humidity engines ran really strong.