<p>The design of high-temperature rotating machinery, such as aero engines and gas turbines, requires precise stress evaluation during transient operating conditions to ensure structural reliability. Despite advances in computational techniques, transient structural analysis remains computationally intensive, posing challenges to efficient design workflows. In this study, we apply PGD to transient thermoelasticity under the small-strain assumption with temperature-dependent material properties by decomposing the displacement field into spatial and temporal modes while accounting for thermal strain. The method is verified for small-deformation linear-elastic problems typical of practical axial-flow rotating machinery. Numerical experiments on industrial-scale applications, including a simplified turbine vane case study subjected to transient thermal loading, demonstrate that the PGD analysis software developed in-house reduces the computation time to approximately one-fourth compared to our in-house FEM software, while maintaining high accuracy. These results confirm the practical effectiveness of PGD for accelerating real-world design workflows in computer-aided engineering.</p>