Abstract: A method of producing polyester filaments by heat drawing with hot tubes comprising shaping by lateral blowing of air the polyester melt extruded through the spinneret; passing the cooled as-spun fibers into hot tubes and heat drawing them; obtaining polyester filaments after the procedures of bundling, oiling, entangling, winding and the like, wherein the hot tube temperature is 80-200° C. and the winding speed is 2500-5300 m/min. The heated hot tube for drawing consists of an internal tube assembly and an electromagnetic induction heating element. The latter is a coil of high temperature resistant metal wire wound on the external wall of the internal tube. In the coil a current is passed, which is controlled by a temperature control circuit of a single return circuit.