A straightforward solution for minimizing the cost of major materials used in motors, such as permanent magnets and silicon steel sheets, is to reduce the motor size as far as possible. However, there is a trade-off between the motor size and temperature rise in the motor that should be taken into account while reducing the motor size. For achieving this, we have been developing an optimal design method based on a combination of a thermo-magnetic field coupling analysis and a direct search algorithm. This paper reports the details of this design method. An outer-rotor, multipole permanent-magnet synchronous motor is the test motor. The results of the torque-density-maximization problem involving constraints on the terminal voltage, coil-temperature rise, and demagnetization of the magnet are shown. The usefulness of our method is also demonstrated.