A system for supporting and cooling a furnace roof comprised of refractory bricks comprises a plurality of roof support members extending across the furnace and being supported from above the furnace roof. The support members are provided with internal channels for circulation of a cooling fluid, and are provided with side surfaces adapted to support rows or refractory bricks between adjacent roof support members. The system eliminates the need to suspend individual bricks from above the roof, and provides simultaneous support and cooling of the roof structure.