An analysis of the cooling problem has been to show by what means the cooling of an air-cooled aircraft engine may be improved. Each means of improving cooling is analyzed on the basis of effectiveness in cooling with respect to power for cooling. The altitude problem is analyzed for both supercharged and unsupercharged engines. The case of ground cooling is also discussed. The heat-transfer process from the hot gases to the cylinder wall is discussed on the basis of the fundamentals of heat transfer and thermodynamics. Adiabatic air-temperature rise at a stagnation point in compressible flow is shown to depend only on the velocity of flow.