:An electromagnetic brake retarder is a device for assisting the brakes of heavy vehicles during descents down long steep inclines. As it operates, a brake retarder heats up and this causes its performance to deteriorate. The retarding force a brake retarder can develop can drop by over 50% as it heats up, and this can lead to a possible “run-away” of the vehicle on which it is installed. Because of this temperature dependency the control of a brake retarder involves two objectives; the first is to maintain the desired vehicle speed and the second is to prevent the retarder from overheating. This paper determines the optimal control of the brake retarder by using dynamic programming.