Abstract <p>This study investigates the temperature, displacement, and thermal stresses in a homogeneous and isotropic three-dimensional thermoelastic half-space solid with varying material properties. Using the Green-Lindsay (G-L) theory of generalized thermoelasticity, the fundamental equations are derived, incorporating temperature-dependent material properties. The medium’s traction-free boundary is subjected to a sudden thermal shock, a scenario frequently encountered in unconventional heat transfer processes. To address this problem, the normal mode analysis and eigenvalue approach techniques are employed to solve the resulting non-dimensional coupled field equations. Numerical results, presented graphically, illustrate the temperature, strain, displacement, and thermal stresses using a suitable material model to elucidate the behavior of the system. A comparison is made with results obtained under the assumption of temperature-independent mechanical properties. The analysis demonstrates the significant impact of the temperature-dependent parameter on the profiles of all physical fields, revealing that a slight increase in this parameter results in a notable decrease in the magnitudes of all field variables.</p>