This paper presents the computation of radiative heat transfer in a slab filled with a participating medium composed of CO2, H2O, and soot. The HITEMP 2010 spectral database is employed to obtain the necessary parameters for the prediction of radiative transfer in the non-isothermal, homogeneous medium. The spectral integration is performed with the spectral line weighted-sum-of-gray-gases (SLW) and the cumulative wavenumber (CW) models and compared with the line-by-line (LBL) benchmark solution. Since radiation heat transfer can sometimes be the dominant heat transfer mechanism in combustion processes, it is important to understand how the predicted thermochemical state depends on the radiation model for the composition, taking into account the complex dependence of the properties with the spectrum. The contribution of this work is to compare two detailed spectral model that are available in the literature and determine advantages and disadvantages in some practical, illustrative examples.