In this paper we study an optimal control problem for a singulardiffusion equation associated with total variation energy.The singular diffusion equation is derived as an Allen-Cahn typeequation, and then the observing optimal control problemcorresponds to a temperature control problem in the solid-liquidphase transition.We show the existence of an optimal control for our singulardiffusion equation by applying the abstract theory.Next we consider our optimal control problem from the view-point of numerical analysis.In fact we consider the approximating problem of our equation, and we show the relationship between the original control problem and its approximating one.Moreover we show the necessary condition of an approximatingoptimal pair, and give a numerical experiment of our approximatingcontrol problem.