I found this on a BMW site. Don't know if this guy's right or not, but here it is.

Forced Induction in general produces heat. 1 psi of compressed air= 25 degrees F. Supercharger's are rated by adiabatic efficiency which is basically a measurement for how well it can compress air without heating it. As far as the gears are concerned, they sit in an oil bath to keep them cool and lubricated. You also have to take into effect what type of blower it is to determine where the compression of air takes place. As far as stock internals are concerned, you need to calculate your effective compression and determine wether or not you engine can handle the excess cylinder pressures. The formula is : boost/14.7 + 1 x static compression.

This is the forum:

How hot can a supercharger get???? - Bimmerforums - The Ultimate BMW Forum