[logfromblammo]

PV = nRT

In a fixed volume (the cylinder, on the time-scale of ignition), pressure is proportional to temperature.

Higher temperature in the cylinder bleeds more heat into the engine block, but also produces more force on the pistons.

Nitrous oxide systems do this, at risk of overheating the engine. If you were to actively drive a Stirling integrated into that engine, it would actively cool the engine, forcing its heat into the cold well. You would overheat your oversized radiator, instead of your engine.