pic: Compressor Cooler

[MrForbes]

It depends on how often the compressor runs. The little compressor is rated at only 9% duty cycle, so if you don't let it cool off for 20 minutes between matches, it can over heat enough to either damage the compressor, or melt the plastic tubing connecting the compressor to the rest of the pneumatic system.

Pointing a fan at the compressor is a good idea. Mounting the fan to the compressor itself to accomplish this, might not be a good idea (and it might be contrary to the rules about modifying pneumatic components)