The Adiabatic Temperature (deg F) equation

http://en.wikipedia.org/wiki/Adiabatic_process#Adiabatic_heating_and_cooling

Homework?

Adiabatic temperature rise, which is what you are looking for, is published by each air compressor manufacturer, as it relates to their compressor. Don't try to mini manage a system, you will grow old very fast.

I take it you are having heat problems coming out of the compressor. They make coolers to solve that equation for you. IF the compressor was bought new, all the factors relating to its performance were calculated in, and the proper cooler was designed to handle it.