The sodium-nickel chloride battery (the ZEBRA cell), and the sodium-sulfur cell, contain beta"-alumina as solid electrolyte. When the cells are charged or discharged; heat is absorbed or released; some of the heat comes from dissipative effects such as joule heating and electrode irreversibility, and some from the reversible reactions at the electrodes. If the rates of heat production in the anode and cathode compartments of the cells are different, thermal stresses could be set up in the electrolyte. In this paper we apply irreversible thermodynamics to quantify these effects.