In this work the temperature evolution, in time and space, in two systems that consist of a single gold nano particle and an ensemble of gold nanoparticles, both embedded in a polystyrene sulfonic acid matrix, is numerically modeled. The heat accumulated by the gold nanoparticles is estimated considering the system irradiation with a nanosecond laser at 532 mn. The distribution of the temperature in time and space is calculated by solving the heat diffusion equations with appropriate initial and boundary conditions. The rise of nanoparticle size determined the temperature increase of the gold nanoparticle and implicitly of the entire system but also the increase of the necessary time for reaching the thermal equilibrium of the system related to the surrounding polymer volume. The temperature evolution and the dynamics of the system towards reaching the thermal equilibrium are influenced by the gold nanoparticles distribution in the polymer matrix.