Controlling a synchronous electric machine includes determining a rotor field current of a wound rotor of the synchronous electric machine and determining a time-rate change in field flux linkage. A rotor field voltage is determined based upon the time-rate change in the field flux linkage, and a rotor field resistance is determined based upon the rotor field voltage and the rotor field current. A rotor temperature is determined based upon the rotor field resistance. Operation of the synchronous electric machine is controlled responsive to a torque command and the rotor temperature.