The invention relates to a furnace (10) for heating preforms (20), of the type that comprises a preform-heating tunnel (12). According to the invention, the tunnel consists of a heating module (18) comprising vertical walls (14, 16) between which the preforms (20) travel. Moreover, at least one wall (16) of the module (18) is provided with at least one heating means (32) which is mounted to supports (34) such that it can move transversely and means (40) for adjusting the transverse position of the heating means (32) comprising at least one member (42) for controlling the movement of the heating means (32) between at least two indexed positions. The invention is characterized in that the control member (42) comprises an indexing boss (54) which can deform elastically such as to fit inside the complementary indexing notches (56, 58) on the corresponding support (34) at proximal and distal positions respectively.