This contribution presents a hybrid analytical-numerical treatment of the thermo-mechanical model for the analysis of the braking process of rotating machine parts such as wheels, etc. The machine parts have the shape of a thick disk. These disks are repeatedly frictionally disk-braked at random sequences of time instants. As the loading is rather severe, the stresses during braking and subsequent cooling reach the plastic limits in compression and tension, respectively. Hence, the loading may cause conditions similar to those encountered in shake-down phenomena.