Furnace and method for operating a furnace

A furnace may include at least two vertical shafts, each of which may have at an upper end thereof an inlet for material to be burnt and at a lower end thereof a burnt material outlet. The inlet and the outlet may be connected by a transfer channel. In each case, at least one main burner may be positioned above the transfer channel, and a cooling gas inlet may be positioned below the transfer channel. At least one additional burner may be positioned below the transfer channel in each of the shafts. Such a furnace can be operated such that the material to be burnt in the currently fired shaft is at least partially calcined in a main burning zone above the transfer channel, and then thermally aftertreated in an additional burning zone positioned between the transfer channel and the additional burner.