The onset of thermoelastic instability (TEI) is known to be directly related to the occurrence of hot spots in a variety of mechanical components such as brakes, seals and clutches. To gain some insight into this failure mechanism, an analytical model for both the symmetric and antisymmetric modes was developed to analyse a friction pair consisting of a conducting body of finite thickness rubbing against an insulating body in the presence of a lubricating agent. The effect of surface roughness, hydrodynamic pressure and viscous shear dissipation within the lubricating film is included in the formulation. The model provided in this paper is general and thus useful for investigating the TEI of a component at the design stage. Several new dimensionless parameters are introduced that allow one to characterize the behaviour of either dry or lubricated systems and their susceptibility to TEI.