An advancing layer or sheet of glass is supported on molten metal and its central portion is selectively cooled by direct conductive and convective heat transfer to and through the supporting molten metal. To accomplish this the depth of molten metal beneath the glass is made to differ across the width of the glass layer transverse to the intended path of glass advance. This controlled heat transfer between the glass and the supporting molten metal is particularly useful in a process wherein the molten glass is delivered onto the molten metal along a substantially horizontal path.