Abstract: A tin bath of a production line for producing flat glass, includes a crown (6) covering a vat (5), in which the liquid tin (10) is located. The crown (6) consists of a self-supporting structure (29) that rests directly on each side of the vat (5), on a supporting framework (25), via a limited, suitable number of sliding or rolling bearings (24). A method makes it possible to limit the longitudinal differential expansion between the crown (6) and the vat (5) such as to prevent deterioration of the luting seams (19) between the vat (5) and the crown (6) that can cause gas leaks between the bath environment and the outside of the vat. The method involves monitoring the longitudinal differential expansion between the vat and the crown by measuring the latter and adjusting the cooling of the vat such as to keep the differential expansion within defined limits.