Conductive heat transfer across an interface between two different materials can be unstable due to the interaction between thermoelastic distortion, contact pressure, and thermal contact resistance. This article investigates the stability of a system consisting of two layers in contact by using a perturbation method. Results are presented for several different material combinations. Most cases exhibit instability only for heat flow into the more distortiue material; but for some material combinations, instability can occur for either direction of heat flow. In all cases, instability is associated with a sinusoidal perturbation whose wavelength is about twice the layer thickness, except for cases of very low interface resistance when wavelengths as small as the layer thickness can be obtained.