An apparatus for tempering plastics material pre-forms with a tempering mould for tempering an outer wall of the plastics material pre-forms, wherein the tempering mould has at least one first mould part which is movable and wherein the first mould part contacts a first wall portion of the plastics material pre-form at least for a time, in order to temper this wall portion. The apparatus has a supply unit in order to supply the plastics material pre-forms to the tempering mould, and this supply unit has a holding device for holding the plastics material pre-forms as well as a movement device which, in order to supply the plastics material pre-forms into the tempering mould, produces a relative movement between the plastics material pre-form and at least one portion of at least one mould part in a longitudinal direction (L) of the plastics material pre-form.