The maintenance of uniform temperature distribution affects the efficiency in most industrial applications. In this study, a novel strategy has been developed for inverse radiative boundary design problems in radiant enclosures with participating medium. This study presents the Backward Monte Carlo method to investigate the inverse boundary design of an enclosure composed of specular and diffuse surfaces. A new optimized Monte Carlo method is proposed to determine the temperature distribution of heaters to achieve desirable prescribed uniform heat flux on the design surfaces. The proposed approach is highly efficient and simple to implement with appropriate results. The evaluated heat fluxes on design surfaces and temperature distribution of heaters are compared with the case where the reradiating walls are assumed to be perfectly diffuse. In the proposed approach, for a specific range of specularity, the absorptivity of the reradiating surfaces does not affect the temperature distribution of heaters. Compared to the diffuse walls, the specular walls have a more uniform temperature distribution and heat flux of heaters. This finding will provide insight into solar furnaces design to enhance temperature uniformity, making specular surfaces suitable in many industrial applications.