Abstract <p>The study investigates the influence of temperature-dependent heat conduction, along with the effects of nonlocality and initial stress, on the nonlinear propagation of plane waves in a transversely isotropic thermoelastic half-space. It aims to understand how variations in thermal conductivity with temperature, combined with nonlocal elastic interactions and pre-existing stress fields, affect wave characteristics and the generation of second harmonic components under generalized thermoelastic conditions. The heat conduction coefficient generally varies with temperature, which plays a crucial role in analyzing the interaction between thermal and mechanical effects in thermoelastic and piezo-thermoelastic materials. This temperature dependence becomes essential to consider, especially at elevated temperatures and in nanostructured materials, where properties like thermal conductivity can no longer be treated as fixed values. In this scenario, a thermoelastic medium is subjected to normal mechanical load applied to its free surface. The plane wave solution is considered as the Poincare expansion in terms of small parameters within in the initial two orders of approximation. The law of heat flux in governing equations introduces the nonlinearity concept in terms of temperature. To&#xa0;determine the temperature distribution, as well as the stress and displacement components, the normal mode analysis approach is employed. The effect of variable thermal conductivity is evaluated analytically on the physical properties. Additionally, the influence of temperature dependency, nonlocality, and initial hydrostatic stress on these parameters is explored. These effects are further illustrated using graphical representations, with numerical calculations carried out through MATLAB-based algorithms.</p>