An apparatus for heating plastic preforms comprises a transport device, which transports the plastic preforms along a predefined transport path. The transport device comprises a first circulating transport device and a second transport device; a plurality of first holding elements constructed and arranged on the first transport device for holding the plastic preforms; at least one heating device along the transport path that heats the plastic preforms during a movement of the plastic preforms along the transport path, wherein the transport path has at least one first portion with a first curvature and at least one second portion with a second curvature which differs from the first curvature; and a plurality of second holding elements constructed and arranged on the second transport device for holding the plastic preforms.