In combination with a furnace having a top from which very hot gases are exhausted, a cooling system comprises an outwardly open collar (12) fixed to the top of the furnace and open inward into the furnace; a tubular exhaust stack (3)adjacent the furnace; a connecting duct (4, 5) extending from the stack and fitted to the collar; a network of heat-exchange tubes lining the top of the furnace (1), the collar, and the connecting duct; and a circulating mechanism for circulating through all of the tubes a coolant (e.g. boiling water) at the same temperature.