What are the specs of that HP computer?
We use HP computers here at work (slowly being replaced by DELL's) and most have 1 80mm case fan installed but it only turns on when the room temps are warm. Most of the time they're not running at all. My work computer is a PIII 500MHz and the fan is mounted in the lower front and it's off most of the time. No exhaust fan, only the power supply fan. The back of the case has a big open grill but I don't know what purpose it serves.
I haven't bought a name brand computer since 1995. Last one was a *gasp* Packard Bell...I didn't know any better at the time.

Cricket