The functioning of thermogalvanic cells has been studied theoretically. The analysis for the simplest case which accounts for only diffusion transport of the reacting substances from one electrode to another has been made. The simple relation for thermodynamic efficiency of such energy sources was obtained. The diffusion-migration transport for the horizontally arranged cell and the diffusion-convection transport for the vertically arranged cell were studied in detail. The original mathematical methods for solving transport equations were used. Analytical results for the concentration distribution and the current-voltage curves were calculated. The principal role of electrode kinetics (fast changing of the equilibrium electrode potential with the temperature) was shown. Finally, the general algorithm for improving thermogalvanic cells was proposed.