The heat conduction equations and sliding contact temperatures of an anisotropic half-space have been investigated. Equations for beth the two-dimensional (band heat source) and three-dimensional (rectangular patch heat source) cases are developed from the basic equations of anisotropic solid heat conduction and subsequently examined using thermophysical properties from typical polymer matrix composite materials of varying continuous fiber orientation and thermal conductivities. The results indicate a significant variation in the interfacial contact temperatures, depending on the orientation of the thermal conductivities. In general, the basic form of the temperature distribution in the plane of contact does not vary with thermal conductivity orientation, however, the magnitude of the relative temperature rise in the contact region does depend on this orientation. When the highest relative thermal conductivity direction is in the plane of contact and parallel to the sliding direction, the relative temperature rise is a minimum and the degree of penetration of heat into the subsurface region is relatively low. When thermal conductivity is highest normal to the plane of contact, or in the contact plane normal to the sliding direction, the relative temperature rise is considerably higher.Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998