We consider the optimal control of a two dimensional steady state thermistor. The problem is described by a system of two nonlinear elliptic partial differential equations coupled with appropriate boundary conditions which model the coupling of the thermistor to its surroundings. Based on physical considerations, an objective functional to be minimized is introduced and the convective boundary coefficient is taken to be the control. Existence and uniqueness of the optimal control are proven. To characterize this optimal control, the optimality system consisting of the state and adjoint equations is derived.