This thesis presents the results of numerical simulations of an InverseCompton scattering model for the photospheric process. We use a Monte-Carlo method to simulate the processing and broadening of Planckian radiation below the Thomson photosphere of hot relativistic outflows. A new numerical code was developed and allowed us to explore a completely new region of the parameter space, in particular a higher and more realistic photon-to-electron ratio. The results may be relevant to the prompt emission of Gamma-ray Bursts (GRBs), Tidal Disruption Events (TDEs), and other high-energy transients where optically thick outflows are present.