The device (1) comprises a tubular cooling tunnel (2), which is traversed from a product in a longitudinal direction during the use of the device and in which an injection nozzle (5) and a tubular secondary cooling section (6) are arranged one behind the other and are viewed in a running direction of the product, where the injection nozzle is designed, so that the product is admitted with cryogenic refrigerant over its entire outer circumference and an atmosphere consisting of mainly cold cryogenic refrigerant is maintained in the secondary cooling section during the operation of the device. The device (1) comprises a tubular cooling tunnel (2), which is traversed from a product in a longitudinal direction during the use of the device and in which an injection nozzle (5) and a tubular secondary cooling section (6) are arranged one behind the other and are viewed in a running direction of the product, where the injection nozzle is designed, so that the product is admitted with a cryogenic refrigerant over its entire outer circumference and an atmosphere consisting of mainly cold cryogenic refrigerant is maintained in the secondary cooling section during the operation of the device. The injection nozzle comprises an annular gap extending itself over a part of the inner circumference of the cooling tunnel, and nozzle openings arranged in equal angle distances around the inner circumference of the cooling tunnel. A flow cross-section of the injection nozzle is changeable. A pre-cooling section (4), into which the refrigerant is supplyable for the purpose of pre-cooling, is provided above the injection nozzle and is viewed in the running direction of the product. The secondary cooling section flowably connects with the pre-cooling section over a gas line to supply the refrigerant from the secondary cooling section into the pre-cooling section. The device has a pre-cooling nozzle directed to a product entrance of the cooling tunnel. A longitudinal axis of the cooling tunn
