In this talk, we will focus on the well-posedness and an optimal control problem for a phase transition problem related to thermal energy storage. Specifically, we want to improve the melting rate of a phase-change material by incorporating hard inclusions with very high diffusivity. This is represented by a semilinear system of three coupled parabolic equations, with Robin conditions on the inclusions' boundary involving the temperatures outside and inside these, i.e. the coupling of the solutions is also effective in the boundary conditions inherent in the system.