In repetitive tasks of an automated handling mechanism, the access motion speed is often limited by the average temperature rise of actuators, especially when the mechanism is directly driven by electrical motors. Thus we developed a method to derive the minimum-time trajectory of a multiple-degree-of-freedom system under the average heat generation restriction. This method is divided into two steps. In the first step, the motion trajectory is determined so as to minimize the cost function including both traveling time and average heat generation of all motors weighted by Lagrangian multipliers. This step is performed based on the Hermite polynomial expression approximation. In the second step, the optimal Lagrangian multipliers are chosen so as to minimize the traveling time. Two typical results of a numerical analysis of a two-degree-of-freedom planar manipulator are presented.