In this paper the effect of radiation, on the overall dynamics of a hot plume above large fires, has been considered. An attempt has been made to give a unified approach to the problem of radiative heat transfer as applied to the phenomena of natural convection. This is obtained by deriving an approximate multi-dimensional transfer equation for heat radiation from the Schwarzschild's equation. The plume material is assumed to be grey and is characterized by a general absorption coefficient. The outside atmosphere is considered calm and is, otherwise, in a state of arbitrary lapse rate variation. The results, given here, are of a more general nature. The solution curves, for some representative values of the parameters, are obtained and are compared with the corresponding ones given in our earlier publications. Also, from the general transfer equation, the asymptotic cases, corresponding to large and small absorption coefficients, are derived.