A heating furnace for heating a sheet of glass therein houses an array of beds for transferring the sheet of glass successively over the beds in the furnace in a first direction toward an outlet opening of the heating furnace while shaping the sheet of glass complementarily to an upper surface of the beds. Each of the beds has a plurality of hot air ejection holes for ejecting hot air to keep the sheet of glass out of contact with the beds. The beds include a final bed disposed near the outlet opening and inclined upwardly toward the outlet opening. The final bed has an upper panel which is upwardly convex in both the first direction and a second direction transverse to the first direction.