Abstract: The invention relates to method and an arrangement for utilizing the heat comprised i the exhaust gas of the combustion chamber of a heating and refrigerating engine working on the basis of a regenerative cyclic gas process by preheating the combustion air supplied to the combustion chamber, with the process gas, which is displaced from the hot working volume or supplied to this working volume, flowing through a regenerator arranged inside of a pressure-proof housing in the region of the hot piston. In order to achieve an effective utilization of the exhaust gas heat without additional apparatus complexity and without insulation of the engine in the region of the warm regenerator while maintaining the temperature profile necessary for the operation of the regenerator, the combustion air to the cooling of the pressure vessel wall surrounding the lower section of the regenerator is used, which cooling corresponds to the lower section of the temperature profile of the regenerator.