In this paper we use the convexity and strong ellipticity conditions in conjunction with the behavior of the material as a definite conductor of heat to establish the uniqueness and continuous dependence results in nonlinear thermoelasticity. By means of the weighted function method we establish the results for unbounded regions exterior to a bounded domain, as well as the half-space and similar regions contained in some half-spaces, provided the boundary is such that application of the divergence theorem remains valid.