An internal combustion engine comprising: ▪ A power shaft; ▪ means for pre-compression and volume reduction (18, 18A, 18B, 18C, 18U) for effecting pre-compression and reduction of volume per mass unit of a working gas, thereby to obtain a pre-compressed working gas at a first pressure; ▪ a positive displacement mechanism having a working chamber partly defined by a movable member coupled to the power shaft, and in which the pre-compressed working gas is successively subjected to: - a heating by combustion near a top dead center of the movable member, at which the volume of the working chamber is minimal; - at least an initial part of an expansion-depressurization, while the movable member moves towards a bottom dead center; - a discharge; ▪ heat transfer means which, during warm engine operation in a lower range of the load levels in which the engine produces driving torque on the power shaft, withdraw heat from the discharged working gas travelling downstream of the discharge of the positive displacement mechanism at a second pressure lower than the first pressure, and yield said heat to the pre-compressed working gas, thereby to cause the temperature of the pre-compressed working gas to be higher at the outlet of the heat transfer means than at the outlet of the pre-compression means; ▪ wherein the pre-compressed working gas, heated in the heat transfer means at a first temperature at a hot outlet of the heat transfer means, is subjected, at least in part in the working chamber, to an additional compression with reduction of its volume per mass unit and increase of its temperature beyond the first temperature in the working chamber before beginning of the heating by combustion, ▪ characterized in that except possibly in at least one depollution apparatus, the discharged working gas is in essentially adiabatic conditions between the discharge of the positive displacement mechanism and a hot inlet of the heat transfer means, in that said engine comprises thermal adjustment means (38, 39, 57, 58, 39U) for moderating the temperature of the pre-compressed working gas reaching the positive displacement mechanism by comparison with the temperature of the discharged working gas available upstream of the heat transfer means when the load level is in intermediate and upper ranges, and in that in the upper range the thermal adjustment means cool down the working gas sent to the positive displacement mechanism, relatively to the temperature of the end of pre-compression. ▪ A power shaft; ▪ means for pre-compression and volume reduction (18, 18A, 18B, 18C, 18U) for effecting pre-compression and reduction of volume per mass unit of a working gas, thereby to obtain a pre-compressed working gas at a first pressure; ▪ a positive displacement mechanism having a working chamber partly defined by a movable member coupled to the power shaft, and in which the pre-compressed working gas is successively subjected to: - a heating by combustion near a top dead center of the movable member, at which the volume of the working chamber is minimal; - at least an initial part of an expansion-depressurization, while the movable member moves towards a bottom dead center; - a discharge; - a heating by combustion near a top dead center of the movable member, at which the volume of the working chamber is minimal; - at least an initial part of an expansion-depressurization, while the movable member moves towards a bottom dead center; - a discharge; ▪ heat transfer means which, during warm engine operation in a lower range of the load levels in which the engine produces driving torque on the power shaft, withdraw heat from the discharged working gas travelling downstream of the discharge of the positive displacement mechanism at a second pressure lower than the first pressure, and yield said heat to the pre-compressed working gas, thereby to cause the temperature of the pre-compressed working gas to be higher at the outlet of the heat transfer means than at the outlet of the pre-compression means; ▪ wherein the pre-compressed working gas, heated in the heat transfer means at a first temperature at a hot outlet of the heat transfer means, is subjected, at least in part in the working chamber, to an additional compression with reduction of its volume per mass unit and increase of its temperature beyond the first temperature in the working chamber before beginning of the heating by combustion, ▪ characterized in that except possibly in at least one depollution apparatus, the discharged working gas is in essentially adiabatic conditions between the discharge of the positive displacement mechanism and a hot inlet of the heat transfer means, in that said engine comprises thermal adjustment means (38, 39, 57, 58, 39U) for moderating the temperature of the pre-compressed working gas reaching the positive displacement mechanism by comparison with the temperature of the discharged working gas available upstream of the heat transfer means when the load level is in intermediate and upper ranges, and in that in the upper range the thermal adjustment means cool down the working gas sent to the positive displacement mechanism, relatively to the temperature of the end of pre-compression.