PURPOSE: To facilitate control of the temperature distribution in the longitudinal and width directions by a method wherein tabular heat ray radiating heaters and the like are disposed in chambers in close opposition and/or in one direction to form a plane or a curved surface, are disposed so as to enable a striplike matter to pass through these gaps and air or a gas substance flows between the heaters and the like and the striplike matter.

CONSTITUTION: A striplike matter 11 is fed in a preheating chamber 5, passes through between blow-off nozzles 31 and 32, passes through between tabular heat radiating heaters 35 and 36 in the state floating in a space by a gas flow blown out of the blow-off nozzles 31 and 32, fed in the following stretching chamber 6 while being heated with heat rays to be heat-stretched in the same manner as that in the preheating chamber 5, then heated in a crystallizing chamber 7 as well and crystallized. The striplike matter 11 which has passes through the plural chambers 5, 6 and 7 is continuously heated to the temperature set in each of chambers 5, 6 and 7. The striplike matter 11 is cooled in the last cooling chamber 15 down to a prescribed temperature by a gas flow from the blow-off nozzles 31 and 32 and a cooling segment and is then wound up on a wind-up machine 21.