The radiation cooler comprises an oblong vertically positioned pressure vessel (1) with a heat exchange element including two sections (10, 11) constituting a central gas passage (12) and a peripheral gas passage (14). For the further cooling of gas and slag there is a second, central heat exchange element (15) positioned in the lowermost portion of the central gas passage (12) and a third heat exchange element (16) positioned in the uppermost portion of the peripheral gas passage (13). The tubes from the second heat exchange element (15) merge directly into the tubes forming the third heat exchange element (16) and both of the heat exchange elements are divided into vertical plane panels (15a, 16a). The tubes forming the heat exchange surfaces (10, 11, 15a, 16a) extend vertically and are welded together to form membrane walls. The heat exchange elements are supported by a common discharge header (20) at the top of the vessel, thereby avoiding supplementary, internal stiffening during transportation of the vessel in a horizontal position as well as during operation in a vertical position. This facilitates also the removal of all the heat exchange elements as a unit upon overhaul.