We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat flux is the control parameter, and the optimality criteria consist of the minimization of the L-2-norm difference of the trace of the solution to the PDE problem at the final moment from the given measurement. Sequence of finite-dimensional optimal control problems is introduced through finite differences. We establish existence of the optimal control and prove the convergence of the sequence of discrete optimal control problems to the original problem bothwith respect to functional and control. Proofs rely on establishing a uniform L-infinity bound, and W-2(1,1)-energy estimate fo the discrete nonlinear PDE problem with discontinuous coefficient.