A cooling method for cooling a wire running along a wire path in a cooling device for cooling a wire, comprising: [a] a first containing chamber for containing a cooling liquid, further comprising: [b] a second cooling chamber comprising a wire inlet and a wire outlet (6, 8) arranged with respect to one another such that they define a wire path and at least one cooling liquid inlet and one cooling liquid outlet (12, 14), [c] cooling liquid driving means fluidically connecting said first and second chambers (2, 4) for driving said cooling liquid from said first chamber to said second chamber through said at least one cooling liquid inlet, [d] said cooling liquid outlet furthermore extending into said first chamber, such that when said cooling device is in operation, the distal end of said cooling liquid outlet is submerged in the cooling liquid held in said first chamber, [e] said driving means and the cross-section of said at least one cooling liquid inlet being dimensioned to project a jet of cooling liquid on said wire path, characterized in that [f] the device further comprises means for introducing inert gas, functionally associated with said second chamber to create an inert gas atmosphere inside said second chamber during the cooling of said wire, and the method further comprises: [h] a cooling liquid projection step, in which at least one jet of cooling liquid is projected on said wire path at a mean speed of at least 0.6 m/s from a distance (d) between the cooling liquid inlet and said path comprised between 6 and 13 times the diameter of the wire that must be cooled, and [i] said projection step being performed in an inert gas atmosphere. [a] a first containing chamber for containing a cooling liquid, further comprising: [b] a second cooling chamber comprising a wire inlet and a wire outlet (6, 8) arranged with respect to one another such that they define a wire path and at least one cooling liquid inlet and one cooling liquid outlet (12, 14), [c] cooling liquid driving means fluidically connecting said first and second chambers (2, 4) for driving said cooling liquid from said first chamber to said second chamber through said at least one cooling liquid inlet, [d] said cooling liquid outlet furthermore extending into said first chamber, such that when said cooling device is in operation, the distal end of said cooling liquid outlet is submerged in the cooling liquid held in said first chamber, [e] said driving means and the cross-section of said at least one cooling liquid inlet being dimensioned to project a jet of cooling liquid on said wire path, characterized in that [f] the device further comprises means for introducing inert gas, functionally associated with said second chamber to create an inert gas atmosphere inside said second chamber during the cooling of said wire, and [h] a cooling liquid projection step, in which at least one jet of cooling liquid is projected on said wire path at a mean speed of at least 0.6 m/s from a distance (d) between the cooling liquid inlet and said path comprised between 6 and 13 times the diameter of the wire that must be cooled, and [i] said projection step being performed in an inert gas atmosphere.