For high speed flows with large material distortions the Arbitrary Lagrangian Eulerian or pure Eulerian frameworks are used. In general, material boundaries will be non-aligned with the computational mesh. For Inertial Confinement Fusion simulations, diffusion of energy across material boundaries is an important physical process to model correctly. In this paper we present two different numerical modelling strategies for solving the diffusion equation with multi-material mixed cells based on the finite volume method. We first present the geometric simple homogenised mixed cell scheme and derive its form from first principles. We next describe the most general multi-material solution strategy based upon treating pure cells and the components of the mixed cells as independent polygons. It will be shown that the homogenised scheme is computationally less expensive than the general approach. However, it will be also shown that the homogenised approach looses accuracy within the mixed cells. To correct for these deficiencies we present several different sub-cell models based on their geometric complexity. By using one-dimensional (1D) and two-dimensional (2D) linear and non-linear applications a process of elimination is used to determine the best sub-cell models with respect to the multi-material scheme. For completeness we present assessments of the relative computational costs of all the different methods with respect to the multi-material scheme.