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The equilibrium temperature distribution in an ideal metal rod, one end of which is subjected to an intense electric field, is studied. Particular attention is focused on the case where the emitting end cools down, and the necessary conditions for this effect are derived. Viewed as a ``heat pump,'' the maximum rate of heat flow as a function of emitter temperature is derived, and it is found that rates in excess of 0.1 cal/sec/cm2 are possible at room temperature if the emitter work function is less than an electron volt.