A known space heater of this type, described in German published specification DE-OS No. 21 39 504, is formed as a unitary elements by compression or injection molding with a generally cylindrical jacket which is closed at its top by an approximately spherical cap and has vanes projecting from its inner and outer peripheral surfaces as indirect-heating elements. A cylindrical combustion pipe projects into the open lower end of the jacket and is provided over its entire height with wall apertures, terminating at a substantial distance from the end cap of the heat exchanger. Also, the ends of the inner vanes lie at a considerable distance from the combustion pipe. Such a structure requires a large outer diameter and is difficult to mold or cast, especially when the number of vanes is high for a maximum heat-transfer rate. This proliferation of vanes with indirect heating effect, on the other hand, goes at the expense of the unobstructed surface of the jacket which alone enables a direct heat exchange between the hot interior and the colder exterior.