An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part aifid a quadratic regularization term. On transforming the associated optimality system to! a generalized equation, an SQP method for solving the optimal control problem is related to the Newton method for the generalized equation. In this way, the convergence of tfie SQP method is shown by proving the strong regularity of the optimality system. Aftjer explaining the numerical implementation of the theoretical results some high precision test examples are presented