In this paper, we consider a special case of the one dimensional heat diffusion across a homogeneous wall. This physical system is modeled by a linear partial differential equation, which can be thought of as an infinite dimensional dynamic system. To simulate this physical system, one has to approximate the underlying infinite order system by a finite order approximation. In this paper we first construct a simple and straight forward approximate finite order model for the true system. The proposed approximate models may require large model order to approximate the true system dynamics in the high frequency regions. To avoid the usage of higher order models, we use a scheme similar to singular perturbations to further reduce the model order.