Here's a top idea - use a Stirling engine that uses the heat from a processor to drive a fan that cools that processor.
Stirling engine design is one of those ideas that feels almost illicit - as a pal put it, "it's damned close to perpetual motion". But it isn't, of course; it relies on nothing more peculiar than the expansion and contraction of gases and the energy flow associated. Put a closed container of gas next to a heat source, and the gas will expand. Let it expand through some form of turbine, and you'll get rotational energy out of it. Then let it cool down, return it to the heat source and off you go again.
The last big attempt to commercialise Stirling engines was by Philips between the 30s and 50s, where devices powerful enough to drive valve wirelesses were built: you heated one bit up using what fuel you had to hand, and bingo, the Empire Service came crackling out of the aether. Those were a technical success but a commercial failure - at the same time as the various European empires were being wound down, thus removing the market of administrators stuck out in the boondocks, some annoying Americans invented the transistor and radios that ran forever on batteries.
So, top marks to MSI for reviving the idea and using it to cool processors - although here's hoping that we'll get chip design down to low enough powers that this Stirling engine too will not be needed.