The hot-gas engine comprises a cylinder, a working piston which together with a cylinder cover delimits a cylinder space designed to accommodate a working medium, a displacement piston which divides the cylinder space into a first and a second working space, as well as a heating device for heating device for heating up the working medium contained in the first working space, and a cooling device for cooling the heated working medium. The working spaces are connected so as to be communicating by way of a regenerator arranged in the displacement piston. The heating device comprises a heating area on the end wall of the working piston, and a heating arrangement associated with the working piston. The cooling device comprises an injection device for feeding liquefied working medium into the first working space. This design provides improved heat supply to the working medium contained in the cylinder, and further provides direct cooling of said working medium. At the same time, a simpler and compact construction of the hot-gas engine can be achieved.