Among engineering systems requiring heat transfer analyses, spheres in a packing structure is one of the more common configuration. A porous medium approach is often used to solve such a complicated system. In fact, it is a useful tool for solving a system involving a large number of spheres, such as in a geothermal system. However for systems containing less spheres, such as in a sintering application, this approach may not be accurate. Recently, a method was developed to solve the mean temperature of contacting spheres in 180 degree orientation. This method used thermal constriction resistances and was able to provide much finer resolution, but contact angles of 180 degree are not a realistic arrangement for spheres in a packing. The present study seeks to extend the earlier formulation to accommodate spheres with varying contact angles. A finite volume formulation was developed using non-uniform grids. Since the grid size must necessarily be small at the contact surfaces, the computation time was significant. To alleviate this, a Multi-Spatial-Temporal Grid Scheme was utilized. A new governing equation has been formulated and verified for packed spheres with varying contact angles. In addition, correlations for the corresponding constriction resistance and the characteristic time parameter have also been developed.