Energy transport in dielectric thin films is mainly governed by the phonon transport across the edges of the film. Depending on the phonon frequencies and the film thickness, some of the phonons do not undergo scattering in the film, which results in ballistic effect on the energy transport in the film. In the present study, the influence of ballistic phonons on the energy transport in silicon thin film is investigated for a spatially varying temperature source at the film edge. The Gaussian temperature distribution at one edge of the film is considered to account for the spatial variation of temperature. The influence of film thickness on energy transport is also incorporated in the analysis. It is found that the Gaussian parameter, defining the spatial distribution of temperature at the film edge, significantly influences equivalent equilibrium temperature variation in the film. Equivalent equilibrium temperature reduces sharply across the film as the film thickness reduces.