An electric power steering apparatus comprising a motor for providing a steering mechanism with steering assist force and a control unit for controlling the drive current of said motor, said control unit comprising: a power self-holding means which can control own power off after power is once turned on by an IG switch; a temperature estimation means for estimating a temperature of said motor and performing a temperature control by an estimated temperature; a temperature estimation status storage means, in a case that a temperature estimation processing continues by said power self-holding means, for storing predetermined data indicating a status of said temperature estimation processing in a storage section within said control unit before said temperature estimation means stops; and an initial value setting means, when said IG switch is turned ON again and said temperature estimation means is activated, for setting an initial value of said estimated temperature based on said predetermined data indicating said status of said temperature estimation processing and a predetermined motor temperature estimation offset value, characterized by; said temperature estimation status storage means is a temperature estimation processing completion flag storage means, at a time point when said estimated temperature has become a predetermined value or less, for storing a temperature estimation processing completion flag indicating that said temperature estimation processing has ended properly in said storage section when said IG switch is turned OFF and said temperature estimation processing continues by said power self-holding means, and said initial value setting means, when said IG switch is turned ON again and said temperature estimation means is activated, checks presence or absence of said temperature estimation processing completion flag, and when said temperature estimation processing completion flag is absent, reads a preset state amount of said temperature estimation processing and sets an initial value of said estimated temperature. a power self-holding means which can control own power off after power is once turned on by an IG switch; a temperature estimation means for estimating a temperature of said motor and performing a temperature control by an estimated temperature; a temperature estimation status storage means, in a case that a temperature estimation processing continues by said power self-holding means, for storing predetermined data indicating a status of said temperature estimation processing in a storage section within said control unit before said temperature estimation means stops; and an initial value setting means, when said IG switch is turned ON again and said temperature estimation means is activated, for setting an initial value of said estimated temperature based on said predetermined data indicating said status of said temperature estimation processing and a predetermined motor temperature estimation offset value, characterized by; said temperature estimation status storage means is a temperature estimation processing completion flag storage means, at a time point when said estimated temperature has become a predetermined value or less, for storing a temperature estimation processing completion flag indicating that said temperature estimation processing has ended properly in said storage section when said IG switch is turned OFF and said temperature estimation processing continues by said power self-holding means, and said initial value setting means, when said IG switch is turned ON again and said temperature estimation means is activated, checks presence or absence of said temperature estimation processing completion flag, and when said temperature estimation processing completion flag is absent, reads a preset state amount of said temperature estimation processing and sets an initial value of said estimated temperature.