Abstract: The apparatus for the heating of fluids exhibits a cylindrical heat exchanging body 10 which exhibits an outer groove 18 for the insertion of a conduit 20 through which the fluid is flowing. The groove 18 forms windings w with a heat transfer length l per winding w. With a fixed section length L to be warmed of the conduit 20, the heat transfer length l per winding w is at least increased by a factor of 1.4 or the heat exchanging cylinder 10 is directed largely horizontally and the diameter of the heat exchanging body 10 is larger or equal to 160 mm. (FIG. 1).