Energy transfer from photo-excited electrons in a metal thin film to the dielectric substrate is important for understanding the ultrafast heat transfer process across the two materials. Substantial research has been conducted to investigate heat transfer in a metal-dielectric structure. In this work, a two-temperature model in metal was used to analyze the interface electron and dielectric substrate coupling. An improved temperature and wavelength-dependent Drude-Lorentz model was implemented to interpret the signals obtained in optical measurements. Ultrafast pump-and-probe measurements on Au-Si samples were carried out, where the probe photon energy was chosen to be close to the interband transition threshold of gold to minimize the influence of non-equilibrium electrons on the optical response and maximize the thermal modulation to the optical reflectance. Electron-substrate interface thermal conductance at different pump laser fluences was obtained, and was found to increase with the interface temperature.