This paper deals with minimum time trajectory optimization along a specified path subject to thermal constraints. We point out here that robots are often integrated in complex robotic cells, and the interactions between the robot and its environment are often difficult or even impossible to model. The structure of the optimization problem allows us to decompose the optimization in two levels, the first one being based on models and results of the theory of the calculus of variations, the second one being based on measurements and derivative free algorithms. This decomposition allows us to optimize the velocity profiles efficiently without knowing in advance the interactions between the robot and is environment. We propose here two numerical algorithms for these two levels of the decomposition which show good convergence properties. The resulting optimal velocity profiles are 5 to 10% faster than classical ones, and have been executed successfully on a real Stäubli Rx90 manipulator robot.