The invention concerns a method for furnace-work production of a string rim (2) portion, which has been extruded on an object, in particular a glazing sheet (1), fixed in a treating station (E), which consists in producing in said portion an accumulation of initially shapeless material (4), which is given a final shape corresponding to the string rim (2) regular cross-section by means of a mobile tool (5), the possible excess material being forced back to be eliminated; producing the mass of material (4) by layering two extruded profile portions, the second portion being deposited after the die (D) has been displaced and repositioned. The invention is characterised in that advantageously the tool (5) is automatically aligned on the string rim (2), immediately after the accumulated material (4) has been extruded and on the travel path on the extrusion die (D), without displacing the object, and is brought into contact with said string rim. The invention also concerns a device specially suited for implementing said method.