For bending a glass sheet so that the glass sheet has a compound curvature, an apparatus comprises a furnace including hearth beds on a bed support and a quenching unit provided with upper and lower air blowers. The final hearth bed may have a top surface with a simple curvature, be provided with one upstream corner cut away thereby defining a cut surface section and arranged in such a manner that the cut surface section is nearly parallel to the hearth bed adjacent to the final hearth bed. Alternatively, the final hearth bed may have a top surface with a compound curvature, so that the glass sheet is bent under the conditions set by controlling a temperature in a downstream part of the furnace, adjusting the inclination of the lower air blower and/or rotating final hearth bed so as to reverse the upstream and downstream ends thereof.