The aim of this paper is to provide upper bounds of the radiation emitted by hot combustion products, mainly CO2 and H2O, and absorbed by some gaseous cold hydrocarbons, or by cold CO2 and H2O. Line by line calculations with accurate spectroscopic data bases are used to compute the absorbed power under two geometrical configurations: a cold optically thin medium surrounded by spherical hot combustion products, and a thin cold slab in front of a hot combustion parallel slab. The absorbed power and the corresponding characteristic time scale are adjusted by simple and physically based formulas to provide quick estimations for various values of combustion product temperature, pressure, and the radius of the hot sphere or the hot slab thickness. The obtained time scales can be compared in a given application to hydrodynamic or diffusive time scales to decide whether it is necessary to take this preheating phenomenon into account or not.