A method and apparatus for spinning, drawing, and winding a synthetic filament yarn, wherein the yarn is subjected during its drawing in a draw zone to a multi-stage heat treatment by heated surfaces. In the first heat treatment, the yarn is heated to the range of the glass transition temperature of the yarn material, and the yarn is guided over the heating surface while partially looping thereabout. The second stage of the heat treatment is formed by an elongate heating surface, and at least one of the heating surfaces is heated to a surface temperature above the melt point of the yarn material. In the draw zone, the yarn is subjected to a tension, which is necessary for a plastic deformation in or directly downstream of the first stage of the heat treatment. In this process, the yarn is drawn and set.