The present invention relates to an annealing furnace (1) for annealing a strand (2) of steel comprising a first heating apparatus (9) for heating the strand (2) during the operation of the annealing furnace (1), comprising a transport device (4, 5, 6, 7) for the strand (2), which is designed to advance the strand (2) in a direction of transport (3) through the annealing furnace (1) during the operation of the annealing furnace (1). The annealing furnace (1) further comprises a first cooling device (13) for cooling the outer surface (17) of the strand (2) with a gas guide (16) in the direction of transport (3) behind the first heater (9), wherein the gas guide (16) is arranged in such a manner that a gas flows along the outer surface (17) of the strand (2) during the operation of the annealing furnace (1) for cooling the strand (2).