A recent study of steady-state thermoelastic contact between two solids has shown that the conventional boundary conditions lead to a lack of uniqueness for heat flowing in one of the two possible directions. Owing to the complexity of the fields satisfying the full equations of thermoelasticity, the resulting solutions are not well suited for investigating the stability of the different states. A model using a much simplified response of a material to stresses and temperature changes is proposed in this article for an eventual study of history dependence and stability in thermoelastic contact.