Finite strain theory has been employed in the past to mathematically describe nonlinear wave propagation phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. In this framework, the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion, are identified as sources of nonlinear effects. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. According to the proposed model, the prevented thermal expansion of the solid leads to thermal stresses that, in turn, produce a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. Emphasis is placed on the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.