An apparatus for thermally bonding together a cover film of an ophthalmic lens package and a base part of the package, including a carrier for supporting the base part with film arranged thereon; a bonding unit above the carrier having a mounting plate with a bonding stamp extending therefrom, the bonding stamp having a mounting portion fixedly attached to the mounting plate, a bonding head arranged beneath the mounting portion with a heatable bonding contour on a side of the bonding head facing the carrier, and an articulated connector arranged between and connecting the mounting portion and the bonding head; and an actuator for performing movement of the carrier and the bonding stamp towards and away from each other for thermally bonding the film with the base part by pressing the heated bonding contour against the film and subsequent separation of the bonding head from the cover film bonded to the base part, the articulated connector being a cardanic joint with two rotational axes.