An apparatus for intensively cooling hot-rolled rolling stock comprising at least one cooling unit for cooling the rolling stock on both sides thereof between two spaced-apart roll stands of a finishing train, the at least one cooling unit comprising on each side of the strip a flow duct with a pressure chamber and a convection chamber for a heat exchange between the rolling stock and the cooling medium by a forced convection for forming a directed flow of the cooling medium and for controlling an intensity of the forced convection in dependence on a flow velocity, further comprising at least one cooling body for cooling the work rolls of a first of the roll stands in a rolling direction of the rolling stock, wherein each cooling body at one of the rolls of the first roll stand defines a gap to which the cooling medium can be supplied under forced convection in the flow area between a cooling water supply and a cooling water discharge, and wherein the at least one cooling unit and the cooling body each have contactless sealing means relative to the surfaces of the rolling stock and the roll to be cooled.