(57) A tape-like object such as a fastener tape the shrinkage curve of which is known traverses a plurality of rollers disposed within a heating unit. In order for the tape to travel through the heating unit in a substantially tension-free state or under a prescribed tension, a suitable feed speed based uponthe shrinkage curve is obtained.The rollers are driven by drive means, responsive to commands from control means, in accordance with the feed speed in such a manner that each roller rotates at a speed different from the other rollers, or in such a mannerthat groups of the rollers each rotate at a speed which is different for each group.