Researchers from Ohio State University says that Spintronics-based chips that run on heat only and are able to process data are possible. The researchers observed that Gallium Manganese can convert heat into spin. They plan to combine spintronics and thermo-electricity(converting heat into electricity) to create chips that run on heat.
Such a "thermo-spintronics" device can be mounted on regular microprocessors - and 'feed' off its waste heat. This will function as both a heat sink and a second processor. This kind of device is "a long way off" though. This can be very useful in large data centers as cooling the heat is a major cost (in 2006, the US spent $4.5 billion powering and cooling down data centers...).