We theoretically predict and calculate non-Joule heating/cooling caused by a direct electric current in ordinary crystalline ice Ih. The cause of this effect is related to partial ordering/disordering occurring in the proton subsystem of ice when protons either drift or diffuse in the ice. Depending on relative directions of the electric current and the configuration vector of ice, the non-Joule effect can be either positive, that is, heat generation, or negative, that is, heat absorption, and its absolute magnitude is usually comparable with that of normal Joule heating. The magnitude of this phenomenon is also approximately inversely proportional to the ice temperature and, thus, is more pronounced at low temperatures.