Thermal radiation within enclosures are widely present in applications such as furnaces, satellites and spacecrafts. Modern demands of quality and efficiency in the design of these structures require better tools than the traditional "trial-and-error" method. In that sense, topology optimization method allows a systemized distribution of material inside a design domain, such that a prescribed objective function is minimized, subjected to design constraints. It represents a robust and reliable option to design the interior of enclosures. Thus, in this work, a topology optimization design method is presented for the distribution of boundary reflectivities within diffuse-gray enclosures. The modeling of radiative heat transfer in a nonparticipating media is solved by the net-radiation method and the optimization algorithm used in this work is the method of moving asymptotes (MMA). The cases considered are the distribution of thermal radiation reflective material on flat surfaces in order to maximize or minimize the sum of net heat flux and to minimize the sum of the temperatures in a specified region of the design domain. Numerical examples are presented to illustrate the proposed design method. (C) 2015 Elsevier Ltd. All rights reserved.