Many mechanical systems rely on the principle of mechanical energy being converted to heat via frictional work, such as brakes and clutches. The demand for increased performance raises the issue of effectively predicting the behaviour. In this paper two mathematical models -a onedimensional pin and a two-dimensional finite element model -are compared in the context of thermo elastic instability of sliding contact. The material parameters that are investigated are the coefficient of wear, thermal dilatation and the specific heat. Both models incorporate temperature dependant wear and friction and exhibit similar response to changes in material parameters and can be used for analysing thermo elastic contact problems. A single value measure has been constructed that quantifies the deviation from evenly distributed contact pressure. Calculating this measure for different values of material parameters has been used to compare the two models. This comparison revealed a difference between the models and to achieve the same evolution of the pressure distribution, the coefficient of wear was changed by a factor of three. When analysing the response to other material properties correction for this discrepancy was made, and the models then showed good agreement.