One of the big problems of modern PC design is cooling. Perhaps the answer is in plain sight - the side of the case.
Just provide a thermal path from the CPU to the side of the case. This may not be easy, but is solvable.
Heat pipes. Overclockers have used them, spacecraft use them - they're proven. A heat pipe with rounded ends and mounts with rounded receptacles and a bit of thermal paste. Conduct heat to the side of the case, and allow for variations of the CPU location.
Thermal strap. Some spacecraft use these, too. They conduct heat well. They are not as multidimentionally adjustable as above, but can be worked out.
At least one side of the case would have to be thermally conductive. Aluminum or copper would suffice. The case side could then be made flat or ridged. The "side" could also be the upper panel of the case, provided you don't really want a big, heavy monitor on top of it. Just imagine a sculpted, polished copper case sitting on top of your desk. A pain to clean, put purty.
The idea takes the concept of shrinking the PC, and also answers another problem - noise. One can eliminate a fan (or more, extend the idea to other components) and gain coolness.
I think I may start designing a case for myself.