An apparatus for the heat treatment of yarns in motion during various operations such as drawing or texturing includes an insulating enclosure which surrounds a heating block, the combination defining a lengthwise channel through which runs the yarn to be treated. Means for guiding the yarn through the channel is provided to ensure the desired positioning of the yarn inside the channel. The heating block consists of a unit comprising at least two cylindrical sections having different diameters and arranged in the extension of one another. The means for guiding the yarn is positioned along the length of the cylindrical sections so that the yarn may be kept at a constant distance from the surface of the cylinder of smaller diameter, with the result that the yarn passing above the smaller cylinder is heated by radiation. The means for guiding then direct the yarn so that the yarn may come into tangential contact with the surface of the cylinder of larger diameter, with the result that the yarn passing over the surface of the larger cylinder is heated by contact or conduction. Suction means for removing fumes produced by the heat treatment operation associated with a sleeve that closes the outlet end of the device is also provided.