For determination as to whether there is a possibility that temperature control satisfying conditions according to an upper limit LH_i and a lower limit LL_i of the annealing control temperatures of annealing object steel sections i will be realized under restrictions on limit values U and D of the control temperature increase and decrease rates, computation is performed without using dynamic programming requiring an enormous amount of data on a continuous annealing line of a steelwork. Annealing object steel sections in an annealing object steel band 12 to be computed are assigned numbers 1, 2, . . . , n in order from the first time division in the direction of movement. T_i is a time required to pass the annealing object steel section i through a predetermined point at which the steel section undergoes temperature control. LH_1=LL_1=b is given. X_i=[IL_i-D*T_i, IH_i+U*T_i] is computed. When X_L_i.sup.1f, Y_i=X_iL_i. When X_i L_i=f, Y_i=X_i. Y.sub.--i is computed from i=1 to i=n in ascending order.