Abstract: A heating and refrigerating machine, especially a Vuilleumier heat pump or Stirling engine, in which a gas-air mixture is combusted in a combustion chamber and the exhaust gas radiates thermal energy to a heater head, which functions as a housing for the hot piston of the machine, part of the outer surface of the heater head forming a portion of the combustion chamber. By using a porous-medium burner and by virtue of its adaptation to the heater head, the transmission of heat by convection and radiation is improved and a compact machine design is attained which transmits heat in a highly efficient manner with low emissions over a broad output modulation range.