OK quick explanation because I'm at work.
The reason air is hot is because molecules in gases are free to bounce around. The more they bounce off of each other, the more energy they release (heat). That's why colder air has a higher concentration of molecules, they don't bounce around as much. When air is compressed to a certain pressure, the distance between molecules is restricted, therefore the amount they bounce off of each other is also constant, so the amount of energy they release is also constant, and bam, you have a certain temperature, unless other factors come into play. In the case of compressed turbo air, there is no other factor until you hit the intercooler.
Feel free to correct or clarify anything I've said here. I'm not a chemist.