The outer circumferential surface of a bottom 4 of a preform 1 and a lower site 3a of a trunk 3 continuous with the bottom 4 is mechanically brought into intimate contact with a cooling pot 16 to undergo reliable cooling. The trunk 3, excluding the lower site 3a of the trunk 3 continuous with the bottom 4, is heated to a predetermined temperature by a heating block 17. When blow-molded, the so treated preform 1 can provide a container having a bottom of a desired thickness and having a uniformly stretched thin-walled trunk.