Basically just the CPU fan, case, and PSU (if you're lucky). If someone can figure out how to get Doom running on just those 3 things, young people will be able to ascend.
I don’t think it would really be any louder than a normal water cooling setup, since you need fans on your radiators anyway. It would just be hideously inefficient compared to radiators, so higher temps. It would be adding like at least 4 thermal transfer boundaries, and heat pipes don’t really work until they get to their operating temperature. So best case scenario, it would probably run a couple degrees warmer than just regular air cooling.