Provided is an apparatus for heating plastic preforms, with a transport device which transports the plastic preforms along a predefined transport path, wherein this transport device has a plurality of holding elements for holding the plastic preform, and with at least one first heating section which is arranged along the transport path, and at least one second heating section which is arranged along the transport path downstream of the first heating section, wherein the heating sections each include a plurality of independently controllable heating elements which allow heating of the plastic preforms in several heating zones, lying above each other in the longitudinal direction of the plastic preforms, with a temperature profile which changes in the longitudinal direction of the plastic preforms, wherein the apparatus includes a control device for controlling these heating sections.