We develop new direction- and frequency-averaged approximations to the equations of radiative heat transfer in glass for optically thick, diffusive regimes. These approximations, which are based on the SP_N  approach given in [E. Larsen, G. Thömmes, A. Klar, M. Seaid, and T. Götz, J. Comput. Phys. 83 (2002), pp. 652--675], represent asymptotic corrections to the familiar Rosseland, or equilibrium diffusion, approximation. Numerical results for realistic problems in the simulation of radiative heat transfer in glass cooling confirm the accuracy and efficiency of the new approximations.