Calculation of temperature in high temperature materials is of current interest to engineers. Aerospace industry encounters cooling problems in aircraft skins during the flight of high-speed air vehicles and in high-Mach-number re-entry of spacecraft. Generally numerical techniques are used to deal with conduction in composite materials. This study uses the exact series solution to predict temperature distribution in a two-layer body: one orthotropic and one isotropic. Often the exact series solution contains an inherent singularity at the surface that makes the computation of heat flux difficult. This singularity is removed, introducing a differentiable auxiliary function that satisfies the nonhomogeneous boundary conditions. An inverse heat conduction technique is used to predict surface temperature and/or heat flux.