A heating device for producing carbon fibers from a thread-shaped fiber starting material, wherein the heating device has a central tubular induction heating element through which the fiber starting material is moved. The tubular induction heating element is surrounded by thermal insulation. At least one mid- to high-frequency induction coil is provided outside the thermal insulation, and an inert gas flows through the central induction heating element, in particular, for carbonizing and/or graphitizing the fiber starting material. For energy optimization, a first and a second tube element is provided on the outer side of the thermal insulation. The elements are made of material that is transparent to the induction field of the mid- to high-frequency induction coil and are spaced apart from one another by an annular gap through which the inert gas flows.