In an open cycle traveling wave thermoacoustic engine, the hot heat exchanger is replaced by a steady flow of hot gas into the regenerator to provide the thermal energy input to the engine. The steady-state operation of such a device requires that a potentially large mean temperature difference exist between the incoming gas and the solid material at the regenerator's hot side, due in part to isentropic gas oscillations in the open space adjacent to the regenerator. The magnitude of this temperature difference will have a significant effect on the efficiencies of these open cycle devices. To help assess the feasibility of such thermoacoustic engines, a numerical model is developed that predicts the dependence of the mean temperature difference upon the important design and operating parameters of the open cycle thermoacoustic engine, including the acoustic pressure, mean mass flow rate, acoustic phase angles, and conductive heat loss. Using this model, it is also shown that the temperature difference at the regenerator interface is approximately proportional to the sum of the acoustic power output and the conductive heat loss at this location.