The transient thermal characteristics of a hot spherical body were investigated when it was suddenly introduced to an initially coal radiatively active medium. The governing equations modeled were solved numerically. The radiative transfer equation was solved by the discrete ordinates method. The results were discussed of changing various physical parameters. The heat transfer mode inside the spherical body was conduction only. But both conduction and radiation were assumed to occur in the medium. Faster cooling of the sphere was accompanied by a decrease in optical thickness, an increase in medium thermal conductivity, an increase in sphere surface emissivity, ora decrease in thermal diffusivity of the sphere. However, faster cooling of the sphere body did not always induce faster heating of the medium. This was found to be dependent on the physical properties of the medium.