An iron is provided having a housing, a soleplate which is to be moved in a displacement direction over a fabric during operation, and a heating element for heating the soleplate, the soleplate having a cooling element for setting at least a portion of the fabric during operation, which cooling element is provided, seen in the displacement direction, behind the heating element. After heating of the fibers in the fabric, the cooling element in the soleplate subsequently cools the fibers in the fabric which are under tensile and compression forces because the soleplate is still in contact with the fabric. This causes the fibers to become set quickly and effectively, which improves the result of the ironing.