• A new configuration of radiant burner is considered. • The study of the effect of heat loss on the stability of the filtration combustion in a porous medium is carried out • Numerical modelling of the combustion inside a burner with axial fuel supply has shown the possibility of stable operation at high temperature levels. • There is a range of pressure drops at which the process of contactless heating of the material to high temperature levels can be carried out. The filtration gas combustion in a porous cylindrical tube with axial injection of combustible mixture is numerically investigated. This configuration can be potentially used as new type of heater for the contactless heating of materials in industrial processes. The material under treatment is placed inside the cylindrical porous tube and is heating by radiative flux from the cylindrical tube wall. The simulation of the filtration gas combustion in porous burner was carried out within the framework of the two-temperature thermal-diffusion model. Conducted numerical modeling yields qualitative description of the effects of heat removal from the burner on the limits of a stable combustion regime. The data about range of the gas flow rates and the intensity of the heat losses on the burner's inner surface corresponding to the stable combustion were obtained. The temperature distributions in the gas and the porous burner were as well gas flow field were obtained in general case, without addresing to the details of the material processing.