I really know little about this but here's my 2p anyway
Only likely idea would be to have the resevoir stored in the fridge, with the water tubes coming out of it and into your PC. If you do this, cut into the rubber air seal around the door - dont cut into the fridge sides/door which are probably a vacuum inside.
I'd expect though the fridge will run loudly and wont last very long, theyre designed to keep cool things cold, not cope with a continual source of heat. Might be an idea to have the hot water get some cooling through a radiator -- even a passive one -- before going into the fridge.