PURPOSE: To improve the transient control accuracy when a water temperature is set by preferentially using a pure water system which is robust and excellent in the cooling ability against the disturbance caused by the variance of the heat valve supplied from an upstream cooling tank.

CONSTITUTION: The pure water temperature Tw0 detected by a temperature measuring resistor 17 is inputted to a heat income/outgo computing part 18 together with the temperature Ts of a strip 9 at the inlet side of an upstream cooling tank 11 which is detected by a radiation temperature 10, the cooling water temperature set value Tw'1 of a downstream cooling tank 1, and the cooling water temperature set value Tw'2 of the tank 11. The part 18 calculates the heat income/outgo to compensate the disturbance of the heat value caused by the heat value supplied from the strip 9 and the water supplied from the tank 11. Then the part 18 calculates the pure water value F1 which is supplied to the tank 1. The value F1 is also inputted to pure water flow rate control part 19. The part 19 calculates a control amount based on the deviation between the value F1 and the pure water flow rate detected by a pure water flow rate meter 20. Then a flow rate control valve 21 of a pure water system is controlled by the output operation of the part 19. Thus the flow rate of the pure water supplied to the tank 1 is controlled.