Abstract: In a domestic energy supply system, the thermal energy of the temperature difference between at least one heat source and at least one heat sink is converted into work by way of a thermal engine. The thermal engine has a fluid cycle with at least two reservoirs, which, in each case as a condenser to be cooled or an evaporator to be heated, are thermally coupled to the heat source or the heat sink. A working temperature difference between the reservoirs of approximately 10° to 200° C. is set at a working temperature of 30° to 280° C. The thermal engine has a hybrid motor in the form of a combination of a pressure media motor and an internal combustion engine, in which firstly a pressure difference of the fluid as a result of the working temperature difference is used for driving purposes and secondly fuel is combusted and converted into work. Furthermore, the invention relates to a method for controlling such a system.