Sandwich and bimetallic plating significantly enhance many engineering applications within the civil engineering, marine engineering, and naval architecture fields due to its high strength-to-weight ratio. However, the design of sandwich plates requires an assessment of how they react to environments in which elevated temperatures are probable. A simple model, consisting of a layer bonded to a half plane, is used to predict the thermoelastic stability of such sandwich and bimetallic plating. It is found that the conduction of heat between the two dissimilar elastic bodies can cause thermoelastic instabilities within the system. The characteristic equation governing the thermoelastic stability of the layer bonded to a half plane exhibits instabilities dependent on the material properties of the layer and half plane. These instabilities are categorized, based on the ratio of the material properties, into three types.