A cooling device for external cooling of a film tube subjected to internal pressure in the production of blown films of thermoplastic material includes a cooling gas ring with a ring housing and a ring nozzle arranged concentrically to a central axis and being open towards the film tube. At least one inner ring channel extending in the circumferential direction about the central axis and being open radially inwards towards the ring nozzle is included. At least one feed channel for supplying cooling gas is attached to the ring housing and connected to the ring channel. The cooling device also includes at least one flow guiding device arranged in the at least one feed channel. When a cooling gas flows through the flow guiding device, at least a partial flow of the cooling gas is set in rotation about a flow axis prior to flowing into the ring channel.