An annealing furnace for annealing a strand of steel. The annealing furnace including a first heating apparatus for heating the strand during operation of the annealing furnace. A transport device advances the strand in a direction of transport through the annealing furnace during operation of the annealing furnace. The annealing furnace also includes a first cooling device for cooling the outer surface of the strand with a gas guide in the direction of transport behind the first heater, wherein the gas guide is arranged in such a manner that a gas flows along the outer surface of the strand during operation of the annealing furnace for cooling the strand.