Techniques for melt spinning and cooling of multifilament polyamide threads are described. The process involves multiple filament bundles spun alongside one another and cooled down separately by streams of cooling air flowing radially from the outside to the inside. Streams of cooling air are produced from a blowing chamber connected to a pressure source. Exhaust gases that occur during the spinning are removed through exhaust openings before the cooling of the filament bundles. An air pressure is set within the blowing chamber in such a way that the exhaust gases in the vicinity of the filament bundles are blown out through the exhaust openings from the inside outwards. A blowing box is assigned a pressure setting means for setting an air pressure within the blowing chamber, by which an air pressure for blowing out the exhaust gases can be set at the exhaust openings of a connection adapter.