<p>This study utilizes the modified extended direct algebra technique to examine the effect of internal heat source phenomena on thermoelastic media with temperature-dependent characteristics, under Green–Lindsay (G–L) theory. The study focuses on nonlinear thermoelasticity, which is of especially essential in a material’s response to fluctuating thermal loads, causing significant changes in both its structural form and inherent properties. This area of research plays a crucial role in accurately modeling real-world behaviors, such as the intricate interaction between thermal and mechanical effects, the performance of materials at different temperatures, and the variation of thermal stresses in large-scale structures. Utilizing the proposed technique, we have derived many exact solutions characterized by distinct free parameters, which include exponential, Jacobi’s elliptic functions, and rational and hyperbolic solutions. Furthermore, to facilitate a better interpretation and understanding of the findings, some of these solutions encompassing stress tensor, displacement, and temperature are displayed on both 2D and 3D plots.</p>