This study develops a novel theoretical framework to model photoacoustic wave dynamics in such media, accounting for the interplay between photothermal, nonlocal thermomechanical, and hydrodynamic interactions. The effects of thermal conductivity variations on wave behavior are rigorously analyzed by integrating the multi-temperature theory with a hydrodynamic semiconductor model. The proposed model employs advanced mathematical techniques, including normal mode analysis and numerical simulations, to derive and solve coupled governing equations for thermal, acoustic, and optical waves. Graphical representations highlight the sensitivity of wave propagation characteristics to changes in thermal conductivity and multi-temperature interactions. Comparative analyses with single-temperature models demonstrate enhanced accuracy and relevance of the multi-temperature approach, especially in predicting wave dispersion and thermal gradients at the nanoscale. The findings offer critical insights into optimizing thermal and acoustic behavior in semiconductor materials, paving the way for advancements in nano-electronic and photonic device design.