A cooling system for use in a shell-type reactor includes vertically extending double tubes with an inner tube and an outer tube closed at its lower end. The system also includes a distributor for supplying a fluid cooling medium into the upper end of the inner tubes and a horizontally extending plate, which on its upper surface includes at least two upwardly open, parallel grooves. Two adjacent grooves are separated by a common inner wall. At least one outer tube, having an upper end, is disposed in each groove, through the plate. Each outer tube is tightly welded to the plate on the groove base. The upper, open side of each groove is closed with a lid, so that each groove forms a collector for discharging the cooling medium from the outer tubes. Each inner tube opens through the lid into a distributor and is tightly attached to the lid.