Abstract: In preset calculation, a plurality of cooling banks are set to be feedforward or feedback banks, and each of water injection amounts in these banks is calculated. In cooling history management, a recalculation position for re-executing the feedback calculation is set. In feedback calculation, a temperature correction value for compensating a delay due to a conveyance time period from a position of the feedback bank to a position of a delivery side pyrometer, and a response delay of the feedback bank is calculated, when a segment reaches the recalculation position. In the feedback calculation, each of water injection amounts in the feedback banks that is calculated in the preset calculation is changed for each of segments based on a delivery side temperature target value, a delivery side temperature actual value calculated for each of the segments, a delivery side temperature prediction value that is recalculated, and the temperature correction value.