A closed cycle regenerative heat engine has a housing (12) defining a chamber (14). A displacer (18) is housed in the chamber. A shaft (24) is connected with the displacer and extends from the chamber. A power piston (30) is housed in the chamber. The displacer (18) is secured to the housing (12) and is resiliently deformable from a rest condition in response to movement of the shaft (24) to displace the working fluid in the chamber. The displacer may be a multi-start volute spring. The displacer (18) may be provided with a heat storage reservoir to store heat received from a working fluid as the working fluid is displaced from a heating location in the chamber (14) to a cooling location in the chamber and reject heat to the working fluid when the working fluid is displaced from the cooling location to the heating location.