We address the problem of the contribution of radiation to the structure and dynamics of accretion shocks on Young Stellar Objects. Solving the 3D RTE (radiative transfer equation) under our "gray LTE approach", i.e., using appropriate mean opacities computed in local thermodynamic equilibrium, we post-process the 3D MHD (magnetohydrodynamic) structure of an accretion stream impacting the stellar chromosphere. We find a radiation flux of ten orders of magnitude larger than the accreting energy rate, which is due to a large overestimation of the radiative cooling. A gray LTE radiative transfer approximation is therefore not consistent with the given MHD structure of the shock. Further investigations are required to clarify the role of radiation, by relaxing both the gray and LTE approximations in RHD (radiation hydrodynamics) simulations. Post-processing the obtained structures through the resolution of the non-LTE monochromatic RTE will provide reference radiation quantities against which RHD approximate solutions will be compared.