A melt spinning apparatus for spinning a synthetic yarn, wherein the yarn is formed by combining a plurality of filaments and wound to a package by means of a takeup device downstream of the spinning apparatus. Downstream of the spinneret, an inlet cylinder with a gas-permeable wall and a cooling tube are arranged. The cooling tube connects to a suction device such that an air stream forms in the cooling tube in the direction of the advancing yarn. This air stream assists the advance of the filaments and leads to a delayed cooling. To ensure adequate cooling of the filaments within the cooling zone, an air supply device is provided for generating an additional cooling air stream which flows in the axial direction of the cooling tube for cooling the filaments downstream of the inlet to the cooling tube.