  We consider an initial and Dirichlet boundary value problem for a semilinear,
two dimensional heat equation over a rectangular domain. The problem is
discretized in time by a version of the Relaxation Scheme proposed by C. Besse
(C. R. Acad. Sci. Paris S\'er. I, vol. 326 (1998)) for the nonlinear
Schr\"odinger equation and in space by a standard second order finite
difference method. The proposed method is unconditionally well-posed and its
convergence is established by proving an optimal second order error estimate
allowing a mild mesh condition to hold.
