The invention relates to a cooling device (100) for cooling at least one element (150, 151) passing through said device, comprising a metal block (115), having a first side and a second side, and comprising a cooling channel (130) for cyrogenic gas. The at least one element (150, 151) can be guided along the sides of the first side of the metal block (115), the cooling channel (130) is at least partially in heat conductive connection with the second side of the metal block (115), and the cooling channel (130) has an attachment (131) on a first end for the entry of cryogenic gas and an attachment on a second end for the exit of cryogenic gas. The invention also comprises a hardening device having such a cooling device (100) and a method for cooling at least one element (150, 151) passing through said device.