Yarn in the form of a yarn wad is passed to a cooling and restraining zone wherein the surfaces of a plurality of balls are pressed directly against the surface of the yarn wad and simultaneously the movement of the balls relative to the yarn wad is restricted so that the balls are prevented from entering the yarn wad and the yarn wad is restrained due to the action of the balls upon the yarn wad. In addition, apparatus is provided useful in the method of the invention.