We consider the optimal control of a parabolic system with respect to the heat exchange coefficient in a newton-type cooling law. We discuss the existence of optimal controls, investigate first and second order optimality conditions and use them to derive an SQP- approach for its numerical solution. We present some numerical results and conclude with an application related to the production of multiphase steels.

(joint work with K. Krumbiegel and N. Togobytska)