Abstract This study investigates the impact of radiative heat transfer on the behavior of flat flame burners within the framework of a simplified one-dimensional model. Flat flame burners stabilize planar premixed flames downstream of a porous plug. Within this study, the porous plug is modeled as a thermally conducting, optically thick medium, allowing for both conductive and radiative heat transfer. Based on the simplified model, the impact of radiative heat exchange between the porous plug exit and the downstream environment is investigated. In “surface” combustion, flame stabilization occurs due to heat transfer between gas phase and porous solid. Results demonstrate that radiative heat transfer from a hot downstream environment to the porous plug significantly increases maximum attainable mass fluxes. For a cold downstream environment, plug properties do not affect the maximum supportable mass flux, although plug porosity and heat transfer between gas and solid have a significant impact on the “stand-off” distance between flame and plug exit. In addition, the model provides insight to a second “submerged” combustion mode, where the flame is stabilized within the porous plug of the burner. Here, increased flame temperatures lead to a dramatic increase of the maximum supportable mass flux. Overall, results show that radiative heat losses play a critical role in both combustion modes: in surface combustion, they are an important mode of heat dissipation, where they can prevent “flash-back” conditions with the flame moving into the porous matrix; in submerged combustion, they prevent flame stabilization close to inlet and exit faces and enable a “slow” solution branch that does not exist without radiative losses.