The transition toward energy-efficient buildings requires integrated thermo-mechanical design rather than purely structural assessment. Construction materials must simultaneously govern stiffness, thermal expansion, and heat transfer without compromising stability. Partial cement replacement enables tailored performance. Pumice powder (PP), rich in amorphous silica, undergoes pozzolanic reactions that refine the concrete microstructure, influencing both mechanical stiffness and thermal conductivity; however, a unified analytical framework quantifying its coupled thermo-mechanical response at the structural level remains lacking. To address this, an analytical framework is developed to evaluate the influence of PP on effective thermo-elastic properties. Homogenized elastic properties are derived using a two-phase model, while thermal parameters are calculated with the Maxwell–Eucken approach. Both sets of properties are incorporated into a refined High-Order Deformation plate Theory (RPT) to determine the critical mechanical buckling load and the critical thermal buckling temperature of structural walls. Predictions are validated against independent experimental data from the literature. At 10% PP replacement, the elastic modulus decreases by approximately 18%, accompanied by a 19% reduction in the critical mechanical buckling load. In contrast, thermal performance improves: the thermal resistance increases by about 18–20%, while the thermal transmittance and heat flux decrease by approximately 17%. Additionally, the critical thermal buckling load increases by nearly 16%. These results quantify the trade-off between reduced stiffness and enhanced thermal stability, demonstrating how PP incorporation modifies the mechanical and thermal instability thresholds of concrete walls.