Abstract: This engine (1) (of the piston engine or rotary Wankel-type engine type) includes a heat-exchanging cylinder head (2) which transfers to the fluid internal to the engine the heat energy collected from an external hot source (liquid, gaseous or by radiation). In a closed or open cycle it uses a gaseous fluid (air) or a refrigerant such as an engine fluid in particular when the temperature of the hot source is low. The volumetric compression ratio of the engine is optimized according to the temperature level of the hot source in order on the one hand to allow the internal heat exchanging cylinder head (2) and (9) to be positioned in the dead volume freed inside the chamber (piston top dead center) of the engine (1) and on the other hand to extract significant mechanical work. It is a matter of increasing technological feasibility at the expense of an acceptable loss in efficiency given that the contribution from the hot source is free of charge.