An electric drive unit for a motor vehicle, comprising: (a) a stub axle; (b) an electric motor having a stator that is fixed with respect to the stub axle and having a rotor that is rotatably supported with respect to the stub axle; (c) a gear system having its input connected to the rotor for torque transmission; (d) a wheel carrier that is rotatably supported with respect to the stub axle and is connected to the output of the gear system for torque transmission; characterized in (e) that air cooling with air circulation is provided for cooling the rotor of the electric motor; (f) and in that the electric motor has provided therein a heat sink for taking up heat from the circulating air.