This talk addresses parabolic optimal control problems in which the objective promotes controls that are piecewise constant in time. That is, optimal controls for these problems have a particularly simple structure. To achieve this we consider controls that are BV-functions in time and use the total variation norm of their derivatives in the objective. This implies that the objective is nonsmooth. We prove existence of optimal controls, derive first- and second-order optimality conditions, provide error estimates, and develop a semismooth Newton method for their solution. Numerical examples are presented as well.