"Lots of extra heat at no extra charge."
What makes you say that? Are you trying to imply that a significant thermal pathway in a case is the cover itself? This is a myth perpetuated by people who sell aluminum cases. Just wondering, I don't like misconceptions.
As for quieting your beasty PC, it depends on what is bothering you about it. If it's fan noise, the best way is to go to the link Mons put up and start reading. There are plenty of power supplies and heatsinks (particularly from Zalman) that do QUITE a nice job of making things more tolerable.
Another major source is hard drive whine. I use an Antec Sonata case for most systems that I build (but not my beast, just 'cause I'm clinging on to the old hag!
) these days. The hard drives are mounted on rubber gromments that significantly subdue most HD's. The system I just built is about as quiet as I can conceive. You could also MacGuyver something similar on your own if you have the time and patience (I did, which is part of the reason I can tolerate my current case).
Of course, if you want to get stupid hardcore, you could always water-cool and have your heat exchanger either be entirely passive (must be very large) or make it remote to the PC and still mostly passive. I built a system for someone that used the full-passive idea. Very cool (literally and figuratively), and totally quiet (not a single fan in the whole case).