Transient heat transfer characteristics of cooling of a spherical body were investigated in the radiatively active spherical medium. Initially the spherical body and the medium were maintained at their constant temperatures. Then heat transfer begains from spherical body to medium. The heat transfer mode inside the spherical body is just conduction. But heat is transferred by both conduction and radiation inside the medium. All the thermodynamic properties were held constant in time. Spherical symmetry is assumed. DOM was adopted to solve RTE. The effect of characteristic optical thickness, conduction to radiation parameter, thermal diffusion strength parameter of spherical body and solid surface emissivity has been studied.