The invention relates to a heating device (H) comprising a heating section (24) for thermally conditioning preforms (1) consisting of thermoplastic material, comprising an upper orifice portion (21) having an opening, a collar-like support ring (54) arranged below the orifice portion (21), and a bottom portion (56) closed at the lower end, to a temperature profile suitable for blowmolding, wherein the heating device (H) has transportation means (33) for the transportation of the preforms (1) along a transportation path (55) of the heating device (H), and wherein the transportation means (33) each bear at least one handling means (41) for holding and handling the preforms (1), wherein a radiation screen (52), which follows the transportation path of the preforms (1), and which has a recess (53) at least on one end face to partially enclose a preform (1) held in the handling means (41) adjoining the recess (53), is provided in an intermediate space between two handling means (41) each provided for handling a preform (1), wherein the radiation screen (52) is arranged such that a surface region of the radiation screen (52), viewed in the longitudinal direction of the preform (1), at least temporarily overlaps on its side facing away with the orifice portion (21) with a surface region of the support ring (54) during the transportation of the preforms (1).