The disclosure is directed to an acoustical heat pumping engine without moving seals. A tubular housing holds a compressible fluid capable of supporting an acoustical standing wave. An acoustical driver is disposed at one end of the housing and the other end is capped. A second thermodynamic medium is disposed in the housing near to but spaced from the capped end. Heat is pumped along the second thermodynamic medium toward the capped end as a consequence both of the pressure oscillation due to the driver and imperfect thermal contact between the fluid and the second thermodynamic medium.