Frictional work in sliding contacts plays an important role in tribology and other related areas. Applications may be found in many engineering fields. Braking of vehicles is almost exclusively done by friction brakes, and thus, understanding of the mechanisms involved is an area of great concern when designing a brake system. From a theoretical as well as experimental viewpoint, little is actually known about the location, magnitude and distribution of pressure and temperature between sliding bodies. This is especially true when considering high energy sliding contacts, such as in brakes and clutches.The present paper concerns the calculation of temperature and pressure distribution between two sliding bodies. More specifically, an instability phenomenon known as TEI (ThermoElastic Instability), which is frequently observed in experiments is investigated. TEI occurs on both the friction material and the opposing sliding material. This is a major cause for excessive temperatures and consequently wear. TEI on the friction material appears as slowly moving contact points. The cause for this is an interaction between wear and thermal expansion. In this paper, the sliding material is modeled as a smooth rigid surface but thermally conductive.To calculate the interface pressure and temperature, a continuum thermomechanical wear model is used. The model can handle temperature dependent variables, such as the friction and wear. The thermomechanical wear model is discretized by finite elements, and to solve the resulting system of equations a Newton type method is used.The model shows promising results and both temperature and pressure distributions are believed to be properly determined. It is also shown, that the motion of the contact points on the friction material is indeed an interaction between wear and thermal expansion. The model can provide qualitative recommendations regarding friction material properties.