A roller hearth furnace in an apparatus for the thermal strengthening of glass sheets comprises a ceramic roller bed having a deviation from a plane of not more than 500, 400, 300, 200, 100, or even 75 or 50 or 30 micrometers over an area of not less than 1, 1.2, 1.3, 1.5, 2, 3, 5 or 10 square meters. Desirably, roller diameters is not more than 75, 50, or even not more than 25 mm. Roller length is desirably not less than 1, 1.2, 1, 1.2, 1.3, 1.5, 2, or even 2.5 meters.