An electric power steering apparatus that enables more precise estimation of a coil temperature by considering a heat transfer phenomenon between a control substrate and a poly-phase coil in addition to a heat transfer phenomenon between respective phases of the coil. The apparatus includes a control substrate that controls a poly-phase motor, a temperature sensor that detects a substrate temperature of the control substrate and a coil temperature estimating section that estimates coil temperatures of respective phases of the poly-phase motor by a motor current of the phase and the substrate temperature based on a heat transfer phenomenon between the respective phases that is caused by a difference in temperature between coils of the respective phases and a heat transfer phenomenon between the coil and the control substrate.