Burning fuels with pure oxygen offers many benefits, including higher efficiency, a CO2-rich flue gas that is suitable for carbon capture, and improved flame stability. However, the extremely high flame temperature that occurs during combustion in pure oxygen is typically assumed to lead to extreme levels of radiative heat flux that are beyond the tolerable limits of boiler materials. This paper presents a unique approach to control wall heat flux under extreme temperatures in particle-laden reacting flows. Fundamental studies were carried out to understand the radiative heat transfer behavior of such systems when temperature and absorption coefficient profiles are dictated by the diffusive-convective characteristics of the system, such as the case of a non-premixed combustion reactor. The results show that if the optical thickness of the particle-laden gas medium is sufficiently large, a considerable amount of emissive power coming from the high temperature sources can be trapped in the medium and the net heat flux on the wall can be managed. An average-temperature approximation (ATA) method is developed to conveniently approximate the wall heat flux when trapping of radiation occurs in an optically dense medium. The ATA method can be utilized to design systems that require manageable wall heat flux via radiative trapping under extremely high flame temperatures. (C) 2016 Elsevier Ltd. All rights reserved.