To precisely predict the temperature of a rolling material when performing cold rolling while cooling the rolling material by a cooling medium before and behind a rolling stand over a plurality of passes.

With the temperature of the rolling material 1 charged into the rolling stand 2 defined as an inlet side temperature T1, the actually measured temperature is set in the pass of an initial time and an exit side temperature predicted in the pass of the previous time is set in the passes of the second and subsequent times. The mill front temperature T2 just before rolling is predicted based on the inlet side temperature T1 and the heat transfer from the rolling material 1 to the cooling medium 3. Next, the post-working temperature T3 right after the rolling is predicted based on the mill front temperature T2, the mill motor output, the heat capacity of the rolling material per unit hour and the heat equivalent of work. Further, the outlet side temperature T4 when the rolling material is discharged from the rolling stand 2 is predicted based on the post-rolling temperature T3 and the heat transfer from the rolling material 1 to the cooling medium 3.