In order to clarify the effect of thermal conductivity on non-Newtonian thermal elastohydrodynamic lubrication (EHL) in the point contact with longitudinal roughness on one surface or on both surfaces, numerical calculations are carried out. The contact is formed by ceramics and steel. The surface shapes of both contact solids are investigated separately. It was found that the pressure at ridges shows lower than that at grooves when the speed of a material with low thermal conductivity is faster than that of a material with high thermal conductivity. In the opposite case, such a phenomenon never occurs. This abnormal pressure variation is largely affected by the combination of contact materials and running conditions.