This paper explores the mathematical modeling of thermoelastic stress in a perfectly clamped metallic rod using the Adomian Decomposition Method (ADM). The study focuses on formulating and solving the governing partial differential equations (PDEs) that describe the stress distribution within the rod when subjected to thermoelastic deformation. By employing ADM, we decompose these complex PDEs into a series of more manageable components, facilitating an analytical or semi-analytical solution without the need for linearization or perturbation techniques. This approach enhances computational efficiency while maintaining high accuracy in capturing the nonlinear behavior of thermoplastic stress. Furthermore, we examine the broader applicability of ADM in solving PDEs across various engineering and physical sciences domains, emphasizing its effectiveness in handling nonlinear problems and improving solution precision.