The energy equation governing a diffusive generator of Cartesian geometry is derived for azcomponent of uniform magnetic field only and for currents and driving forces in thex‐yplane only. The kinetic coefficients may depend on temperature in any manner. Only the induced magnetic field is neglected. Steady state is assumed. Heat is forced to flow in theydirection and current is allowed to flow in thexdirection. By assuming no current in the heat flow direction, and no temperature dependence in the current direction, the current is eliminated from the energy equation, which is then the differential equation for the temperature distribution with arbitrary temperature dependence of the coefficients. The exact temperature and current profiles and the efficiency expression are then worked out in analytic form for temperature‐independent coefficients. The magnetic‐field dependence of the coefficients is then calculated assuming classical statistics, and a single carrier. Numerical integrations are done only for scattering by ions. The upper limit of the efficiency is displayed for various magnetic field strengths as a function of driving‐temperature differences.