Methods of making glass include the steps of providing a glass melt in a first melting furnace and flowing the glass melt through a connecting tube from the first melting furnace to a second melting furnace. The methods further include the steps of heating the glass melt within a first area of the connecting tube with a first heating device and heating the glass melt within a second area of the connecting tube with a second heating device. Apparatus for making glass are also provided with a first melting furnace, a second melting furnace, and a connecting tube connecting the first and second melting furnaces. Example apparatus include a first heating device configured to heat the glass melt within the first area of the connecting tube and a second heating device configured to heat the glass melt within the second area of the connecting tube.