Abstract: In a Stirling engine with a cylinder head which can be heated, with a plurality of heating pipes bent in approximately U shape and with a cooler the the heat transfer to the heating pipes and the efficiency of the cooler are improved. This For this purpose the outwardly directed pipe sections (4c) of the heating pipes (4) through which the working medium flows are provided at least locally with a ceramic backing (11) for optimization of the flow (10) of the heating gas and the cooler is in the form of a light metal body (20) with radial ribs (23) within a pot-like housing (21), through which cooling water flows. The spacing of the radial ribs (23) from one another is greater than the gap (25) between the pot inner wall and the outer radial ribs bounding wall.