The invention relates to a heat exchanger (1) for an annealing furnace for exchanging heat between two fluids, comprising a tubular profile which comprises heat exchanger fins on its outside jacket and which is associated on at least one face side (3) with a connecting flange (4) with at least one flow opening (8) for one of the two fluids, especially a hot gas. In order to provide advantageous constructional conditions it is proposed that the profile is a profile tube made of a folded sheet whose heat exchanger fins (7) aligned in the longitudinal direction of the profile are formed by the corrugated profile, especially the corrugated flanks, of the folded sheet.