The method and the device are used to blow-mold containers. A preform made of a thermoplastic material is first subjected to thermal conditioning in the area of a heating section along a transport path. Then the preform is shaped into the container inside a blow mold using blowing pressure. At least sections of the transport path are delimited in a tunnel-like manner. A cross-sectional area of the heating section arranged transversely to the transport path is changed according to a dimensioning of the preforms to be heated. The change occurs in such a way that a smaller cross-sectional area is associated with smaller preforms than with larger preforms.