Thermal diffusion in the metal oxide semiconductor field effect transistor has received increased attention across a number of disciplines in recent years. This paper studies a three-dimensional (3D) heat conduction process in a MOSFET device based on Silicon (Si) and Graphene (Gr) materials. In order to perform analyses, a mesoscopic method was applied, based on lattice Boltzmann method (LBM) with D(3)Q(15) model accounting the specularity parameter effects. The present study found that the maximal temperature is spotted at the interface whose value is 308.7 K and 324.5 K for the Gr-FET and Si-MOSFET, respectively, at t = 30 ps and p = 0.5. Also, the obtained results indicate that the specularity parameter has an important role in the phonon heat transport and thus in reducing the temperature in the nanotransistors. The preference of graphene device and the unique properties of graphene material make this material a good candidate for future nanoelectronics systems generation.