is provided for spinning a multifilament thread from a thermoplastic material including the steps of extruding the melted material through a spinneret with a plurality of spinneret holes into a filament bundle with a plurality of filaments winding the filaments as thread after solidifying and cooling the filament bundle beneath the spinneret whereby in a first cooling zone the gaseous cooling medium is directed in such a way that it flows through the filament bundle transversely the cooling medium leaving the filament bundle practically completely on the side opposite the inflow side and in a second cooling zone beneath the first cooling zone the filament bundle being cooled further essentially through self suction of the gaseous cooling medium surrounding the filament bundle application_number US 73257310 A description the method thus deals with a two step cooling procedure in the first step a gaseous cooling medium flows through the filament and the cooling agent leaves the filament bundle practically completely on the side opposite the inflow side in this step of the cooling process the cooling medium should thus not be drawn along with the filament if possible to execute this first cooling step the gaseous cooling medium may be directed to flow through the filament bundle transversely to the direction in which the filament bundle is moving so that a so called transverse air flow is provided this air flow can be effectively created by sucking off the gaseous cooling medium with a suction device after it has passed through the thread bundle a well directed cooling stream is thus achieved and it is ensured that the cooling agent quantitatively leaves the filament bundle.