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The amount of computation you can carry out on the surface of a planet is proportional to the temperature cubed.
As Eliezer and Nate often repeat when explaining the dangers of superintelligence, the hotter you run, the more energy you dissipate. To be exact, the amount of energy radiated is proportional to T^4, known as Stefan--Boltzman law. But also, the hotter you run, the more energy it takes to perform computation, and linearly so (see Landauer's limit). So the overall dependence is cubic. I didn't have this fact cached before and thought it would be neat to share.