The interaction and surface features between point contact surfaces composed of longitudinal roughness with infinite or finite length and transverse roughness were discussed based on a transient non-Newtonian thermal elastohydrodynamic lubrication (EHL) model. Each surface shape is greatly affected by the difference in elastic moduli, thermal conductivities, and velocities of both contact surfaces. There is a large difference in pressure behavior when the transverse roughness is in contact with the longitudinal roughness with finite length and when it is in contact with the longitudinal roughness with infinite length. In the contact between surfaces with infinitely long longitudinal and transverse roughness, the friction coefficient is lower when the surface with longitudinal roughness has a low thermal conductivity than when it has a high thermal conductivity. Furthermore, the pressure fluctuation is larger when the transverse roughness surface has a high thermal conductivity than when it has a low thermal conductivity.