Abstract: The process is used for tempering preforms made of a thermoplastic material; the preforms are to be blow molded. The preforms are provided with a temperature profile along a circumference. The temperature profile is generated by differentially heating strip-shaped regions, which extend in the direction of a longitudinal axis of the preform. A step-by-step tempering for the purpose of temporally sequential thermal conditioning of different regions of the preform is carried out with movement phases and rest phases. A carrier device is rotated by the interactions of a gear and a matching gear for initiating rotational movements. The preform is moved, motionless with regard to the rotational direction, through the tempering zone at least along a portion of the transport path before the start of the engagement of the gear with the matching gear.