The heat exchanger has an axis and at least one heat-exchange body (5) encompassing said axis, annular in cross-section and comprising sheet metal elements (23, 27) which are present in succession around the axis and are involute in cross-section and between which edge strips (24, 25, 28, 29) welded to said sheet metal elements alternately at their involute side edges (23c, 23d, 27c, 27d) and at their inner and outer edges (23a, 23b, 27a, 27b) are arranged and which alternately bound passages (33, 34) for a first and a second fluid (15, 16). Each passage (33, 34) contains an intermediate layer (31, 32) which consists of a knitted wire fabric. The edge strips (24, 25, 28, 29) and the knitted wire fabrics hold the successive sheet metal elements (23, 27) in a stable and durable manner a distance apart and result in only little thermal conduction in the direction of flow.

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