Material properties are one of our limiting factors for power output. A cool chamber sucks heat (ie, energy) out of the combustion gases - this heat is driving the pressure we use to extract work.
A hot chamber doesn't suck up so much energy from the hot gas. However, our materials (and manufacturing tolerances) dont allow us to exceed certain temperatures before things get too big and lock up (ie, seizes) or the parts weaken too much and fail. Another way to look at it is if we used a strong insulator for the motor instead of metal; this way no heat is added to the intake charge, and no heat is lost during power stroke (wiki "otto cycle" and "carnot cycle"). The only heat lost is through the exhaust gas.
Watercooling is better than air cooling because we can extract more heat; This allows us to release more heat and extract more power without material failure, even though we're shedding most of the energy through the radiator and not the rear wheel.
the motor being cooler is not the reason it's better - it's the ability to remove all the waste heat. In theory a hot engine will get more power from a given amount of fuel, but to trump a watercooled system the thing would need to be made of silicon or a composite like what they use for turbos (I forget the name of it)
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