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No, if the rest of the body was at zero K and the outer surface was at 1k, the body would cool till it reached zero K throughout. There would have to be an input of energy from somewhere to keep the surface at 1K. In a closed system, like we believe the universe to be, where there's no energy input from "outside", the body must obey the laws of thermodynamics, so it would cool till it reached equilibrium.
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