Can it be harmful for your computer's processor to be running a program like Folding all the time? I've noticed that with Folding running, my computer's fan is constantly running at the highest speed, clearly because it is cooling down a very active processor.
I just don't want to damage my computer.
Not unless you built your PC yourself and choose a heatsink that is horribly undermatched to your processor -- in which case the thermal shutdown switch would be triggered on your processor. When processors get too hot, they have a built-in safety in that they will cut all power and immediately shut down before they overheat and become damaged.
If you want your computer to run cooler and with a fan that is less loud -- using the Windows GUI folding client, you can cut your CPU useage down from 100 to say 75 or 50. This will of course cut down on how fast your machine turns out work units.