This article surveys recent results regarding the existence of weak solutions to quasilinear partial dierential equations (PDE) coupled nonlocally by the integral operator of the radiosity equation, modeling conductive-radiative heat transfer. Both the stationary and the transient case are considered. For the stationary case, an optimal control problem with control constraints is presented with rst-order necessary optimality conditions, where recent results on the solution theory of the

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... ed state equation allow to close a previous gap. A-nite volume scheme for the discretization of the stationary system is described and, based on this scheme, a numerical computation of the temperature eld (solution of the state equation) is shown as well as the numerical solution to a realistic control problem in the context of industrial applications in crystal growth.