The heat transfer coefficient between two elements of a thermoacoustic device is defined as being the ratio between the rate of heat flow between them and the temperature difference occurring at the interface. Previous experiments have demonstrated that this quantity is proportional to the amplitude of acoustic oscillation. For stack and heat exchanger duct widths that are comparable to the thermal penetration depth, the heat transfer coefficient was found to be equal to that predicted by a theory based on the elements of the engine being perfect heat exchangers. Results of experimental measurements of the variation of heat transfer coefficient as a function of frequency will be presented. Increasing the frequency reduces the thermal penetration depth allowing the effects of partial thermal contact within the elements to be evaluated. These results will be compared to attempts to build theoretical models of the heat exchange process.