Rotary electrical machine for a motor vehicle, wherein said rotary electrical machine comprises: a) a rotor which is supplied by an excitation current (ie); b) a stator which comprises a polyphase winding, and is coupled to said rotor; c) a thermal protection module which is designed to evaluate at least one temperature in the rotary electrical machine, and to compare the said at least one temperature with an associated thermal protection threshold (Th); d) a device for control of the rotor which supplies the excitation current (ie) according to an operating mode command received from a motor control unit of said motor vehicle, and according to said temperature comparison, such as to make the rotary electrical machine operate according to an operating mode from amongst: e) a nominal generator mode, in which the machine is configured to provide a first maximum power; or f) at least one extended generator mode (M2, M2'), in which the machine is configured to provide a second maximum power greater than said first maximum power, characterized in that the control device being designed to limit the excitation current (ie) of the rotor, in order to make the rotary electrical machine operate in the nominal generator mode if its temperature is higher than the associated thermal protection threshold (Th) and the control device being designed to increase the excitation current (ie) of the rotor, in order to make the rotary electrical machine operate in the extended generator mode (M2, M2') if its temperature is lower than the protection threshold (Th) determined, and if the control device receives an operating mode command in extended generator mode (M2, M2'). a) a rotor which is supplied by an excitation current (ie); b) a stator which comprises a polyphase winding, and is coupled to said rotor; c) a thermal protection module which is designed to evaluate at least one temperature in the rotary electrical machine, and to compare the said at least one temperature with an associated thermal protection threshold (Th); d) a device for control of the rotor which supplies the excitation current (ie) according to an operating mode command received from a motor control unit of said motor vehicle, and according to said temperature comparison, such as to make the rotary electrical machine operate according to an operating mode from amongst: e) a nominal generator mode, in which the machine is configured to provide a first maximum power; or f) at least one extended generator mode (M2, M2'), in which the machine is configured to provide a second maximum power greater than said first maximum power, characterized in that the control device being designed to limit the excitation current (ie) of the rotor, in order to make the rotary electrical machine operate in the nominal generator mode if its temperature is higher than the associated thermal protection threshold (Th) and the control device being designed to increase the excitation current (ie) of the rotor, in order to make the rotary electrical machine operate in the extended generator mode (M2, M2') if its temperature is lower than the protection threshold (Th) determined, and if the control device receives an operating mode command in extended generator mode (M2, M2'). e) a nominal generator mode, in which the machine is configured to provide a first maximum power; or f) at least one extended generator mode (M2, M2'), in which the machine is configured to provide a second maximum power greater than said first maximum power, characterized in that the control device being designed to limit the excitation current (ie) of the rotor, in order to make the rotary electrical machine operate in the nominal generator mode if its temperature is higher than the associated thermal protection threshold (Th) and the control device being designed to increase the excitation current (ie) of the rotor, in order to make the rotary electrical machine operate in the extended generator mode (M2, M2') if its temperature is lower than the protection threshold (Th) determined, and if the control device receives an operating mode command in extended generator mode (M2, M2').