[t vago]

Cylinder compression is modelled as an adiabatic (no heat energy transfer) process. We ignore real-world losses to the combustion chamber surfaces, because cylinder compression typically happens fairly quickly, and because the real-world losses that do occur in this short period of time will not substantially affect the temperature of the compressed air.

Therefore, T1*V1^(gamma - 1) = T2*V2^(gamma - 1)
or
T1 / T2 = (V2^(gamma - 1))/(V1^(gamma-1))
or
T1 = T2 * (V2 / V1)^(gamma - 1)

The quantity (V2 / V1) is also known as the compression ratio. So,

T1 = T2 * CR ^ (gamma - 1)

So, let's set T2 = 32 F or 0 C or 273.15 K. Let's set CR to 9.5. Let's set gamma to 1.4 for air.

T1 = 273.15 K * 9.5 ^ 0.4
T1 = 672.2 K or 399 C or 750 F

Note that the presence of gasoline will lower this temperature somewhat. As the air temperature inside the cylinder rises, it will rise above the evaporation temperature of the gasoline. The gasoline will then absorb heat energy from the air in order to vaporize. This is why extra gasoline is squirted into cylinders at wide open throttle - The gasoline "cools off" the fuel/air mix such that detonation is avoided.

This cooling effect is also why water injection is popular as an anti-detonation mechanism. Water tends to take over 2 times as much heat energy to vaporize as does gasoline. Charge temperatures are reduced by about this much with a water injection setup, as compared to gasoline alone.

It is unrealistic to compare an engine to an air compressor. Water entrapment inside an air compressor is a consequence of concentrating water content as a result of gathering the compressed air inside a pressure vessel. At some point, the water vapor present in the compressed air will exceed the saturation point of that compressed air, and water will condense out.