In this paper, a two-dimensional heat diffusion system modelled by a partial differential equation (PDE) is considered. Finite order approximations are constructed first by a direct application of the standard finite difference approximation (FD) scheme. Using standard tools, the constructed FD approximate models are reduced to computationally simpler models. Further, alternative approximate models are proposed using the asymptotic limits of the FD approximations. Numerical experiments suggest that the proposed alternative approximations are more accurate than the FD approximation.