In a wire insulating line, a cooling device that cools down a traveling high-temperature linear material, which is resin-coated by an extruder, in cooling water includes a reservoir tank that reserves the cooling water and allows the linear material to pass therein, and water spray nozzles that are provided in plural numbers in the reservoir tank with a gap along the linear material traveling direction and spray water to the linear material in the cooling water. Further, in the wire insulating line, a coated wire haul-off machine includes front and rear capstans for winding the coated wire, which comes out of the reservoir tank and on the way to a take-up machine, by allowing it to reciprocate back and forth for several times, and a water film flow forming groove body to form water film flow for cooling, which is arranged between the front and rear capstans and extends along a lower coated wire traveling path between the front and rear capstans, in which the haul-off machine is constituted that the coated wire is allowed to travel in the water film flow between the front and rear capstans.