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In this article a spectrally resolved solution of the integrated radiative transfer equation for the discrete transfer method with linear temperature interpolation is presented. Combined with the discrete ordinate method, the radiative heat fluxes are determined for use in the finite-volume energy equation. The spectral dependence of the absorption coefficient is approximated as a series of bands of constant value and scattering is neglected. The method is shown to be computationally efficient when applied to a course mesh typical for conduction problems and at the same time to be accurate for both optically thin and thick media, including semitransparent media.