Abstract: To cool a strip rolled by a hot rolling mill using cooling banks installed on the run out table at the delivery side of the hot rolling mill, and to control the strip temperature in front of coiler to a preset target temperature, the strip is conceptually divided into segments or cooling units which have a length equal to the length of a single cooling bank, the temperatures of the segments are predicted, and the cooling banks are so controlled as to have the prediction temperatures coincide with preset target temperature. In this case, a feed-forward control of the cooling water flow rate in the cooling banks are made so that predictive temperatures on a real time basis of the temperatures of the cooling segments at the time when the segments are staying in the respective cooling banks coincide with the target temperatures.