A friend and I baked some YCBO superconductors back in college. They superconducted just fine in a liquid N environment. Levitated magnets pretty well too, because as a magnet approaches the surface of the superC, the changing B (magnetic) field induces a circular current. That current in turn creates an opposing B field that pushes back on the magnet. Very cool to actually watch it happen (I know... taking geek to the next level)!
The heat from CPUs comes from current traveling through a resistance. Plain-and-simple. That resistance is in the wire traces, poly-Si traces / gates, and transistor channels on the chip. The highest resistance is in the channels (especially the p-transistor channels), then the poly-Si, then the metal traces. The current that travels through the resistance is either switching current or leakage current. These guys are proposing to reduce the leakage current, but that still won't solve the problem of switching current, which is tied to V^2, C, F, and a couple of other factors that depend on the nature and purpose of the IC. To solve heat-induced switching current, you need to replace the Poly-Si and channel materials with lower-resistance materials that will also enable you to lower V, or else you need to make C lower by generally making everything smaller. Only so far you can take that with Silicon.