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An electrically operated power steering apparatus for an automotive vehicle having a steering wheel to be operated by the vehicle operator includes a motor and a power supply restricting device. The motor applies a drive force thereof to a torque transmitting system so as to assist a steering torque applied to the steering wheel by the vehicle operator. The power supply restricting device utilizes a temperature of a heated portion of the electrically operated power steering apparatus which emits heat as a result of a supply of an electric power to the motor, at a reference point of time, as an initial temperature of the heated portion, utilizes a plurality of electric power-related values each of which is related to at least one of a current and a voltage value of the motor, as a plurality of physical quantities related to temperature increases of the heated portion each of which is an increase of the temperature of the heated portion from that at the reference point of time, and restricts the electric power supply to the motor such that an actual value of the temperature of the heated portion does not exceed a predetermined upper limit thereof.
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