A heat-insulating lining on heat exchanger surfaces for reducing the heat flow at the cooling surfaces of a medium- or high-pressure heat exchanger, which comprises a tube-web-tube wall. Corrosion resistant fastening pins are arranged in a weld area on the webs of the cooling surface. A ceramic fiber material is arranged as a heatinsulating material on both sides of the webs up to the level of the outside of the tubes of the tube wall, and segments of a ceramic moleskin mat, which are held by fastening pins and fastening washers, are arranged above it on both sides. An expanded metal, which is protected by a refractory material with good corrosion resistance, is additionally arranged at one or both edge zones and at the locations of the joints of the moleskin mat segments.