The role of radiative energy transfer on turbulent boundary layers is carefully analyzed, focusing on the effect on temperature fluctuations and turbulent heat flux. The study is based on direct numerical simulations of channel flows with hot and cold walls coupled to a Monte-Carlo method to compute the field of radiative power. In the studied conditions, the structure of the boundary layers is strongly modified by radiation. Temperature fluctuations and turbulent heat flux are reduced, and new radiative terms appear in their respective balance equations. It is shown that they counteract turbulence production terms. These effects are analyzed under different conditions of Reynolds number and wall temperature. It is shown that collapsing of wall-scaled profiles is not efficient when radiation is considered. This drawback is corrected by the introduction of a radiation-based scaling. Finally, the significant impact of radiation on turbulent heat transfer is studied in terms of turbulent Prandtl number. A model for this quantity, based on the new proposed scaling, is developed and validated.