[jacquesm]

You can't cool from the inside of that cube without having some way of transporting the heat out of it.

All you'd end up doing is heating that inside up to the temperature of the dies and after that there would be no more cooling effect (and this would happen in a few seconds after starting the whole thing up). You could do an 'inverse' of this by cooling the dies from the outside and having the interconnects in the space in between. This would still require a lot of cooling and there would be an issue with connecting the resulting assembly to the underlying PCB.

[jonhendry18]

I think woah means that the top would be open. So instead of a cube it'd be an open box. A heat sink (or arrangement of peltier coolers attached to a fan and heat sink, or whatever) would fit down into the box and be in contact with the five core-containing sides.

[blackflame7000]

What if you used electronic cooling to chill a copper thermal conductor?

[jacquesm]

Electronic cooling? Do you mean Peltier elements? They have a 'hot' and a 'cold' side, and their capacity is handily outstripped by any modern CPU. If that worked we would be using Peltier coolers to make quiet PCs today, after all, that problem is only 1/5th as complex.