The purpose of this work is to analyze the heat transfer characteristics of VascomaxC300 during high-speed sliding. This work extends previous research that is intended to help predict the wear-rate of connecting shoes for a hypersonic rail system at Holloman Air Force Base. Solutions were generated using finite element analysis, finite difference methods, and spectral methods. The frictional heat generated by the pin-on-disc is assumed to flow uniformly and normal to the face of the pin and the pin is assumed to be a perfect cylinder resulting in two-dimensional heat flow. Displacement data obtained from the experiment is used to define the moving boundary. The distribution of temperature resulting from transient finite element analysis is used to justify a one-dimensional model. The one dimensional heat equation is solved with variable parameters using a variable-step, variable-order, implicit finite-difference method. Spectral methods are then employed to calculate the spatial derivatives improving the approximation of the function which represents the data. It is concluded that a one-dimensional approach with constant heat transfer parameters sufficiently models the high-speed pin-on-disc experiment.