Thermal transport in low density silica aerogels was studied theoretically and experimentally over a wide range of optical thickness and ratio of radiative to conductive heat transfer. Measurements on the combined heat transfer were performed for aerogel densities between 5 and 220 kg m(-3), for temperatures from 100 to 650 K, for internal gas pressures between 10(-4) and 1000 hPa and two boundary emissivities of 0.04 and 0.77. A high precision numerical method for the calculation of the temperature profile and the total (combined) heat flux in these semi-transparent, non-scattering, non-grey media is presented.