Simplistic compressed air temp can be easily calculated by the Ideal Gas Law. PV=nRT. n and R can be considered constants for simplicity, so then we can see that pressure x volume = temperature. This is a basic approximation, but if you take a sealed can of air, and squeeze it super fast to half of the can volume it was (without changing the amount of gas inside), you can see you will double the temp of the air inside.
If you are running say 14.7 psi of boost (double atmospheric pressure at sea level), it should be coming out at double the ambient atmosphere temp. You can add a pinch for turbo compressor heat, inefficiencies, etc....
