<p>A novel theoretical formulation is developed within the framework of generalized thermoelasticity by adding thermomass motion into the modified Green–Lindsay theory. The basic governing equations for an isotropic, homogeneous medium are established to characterize the coupled thermal and mechanical responses. A uniqueness theorem is rigorously proved, ensuring the well-posedness and physical consistency of the corresponding mixed initial boundary value problem. Furthermore, a reciprocity theorem is derived using the Laplace transform technique, and extended forms of the Somigliana theorem and Green’s function are applied to determine temperature and displacement fields. The proposed theory offers a refined understanding of thermoelastic interactions under the influence of thermomass motion as well as relaxation phase effects. Including thermomass motion into the modified Green–Lindsay theory introduces nonlinearities from the inertial and convective nature of heat flux. These effects, arising from flux convection and stress dependence, lead to nonlinear hyperbolic equations that become prominent under rapid thermal loading or high temperature gradients, significantly affecting wave speeds and thermoelastic behavior. This theorem provides valuable insights into the mutual influence and interaction between different aspects of the system under consideration.</p>