Abstract: A control method comprises predetermining a or presuming a fuel flow rate for each of three control zones of a continuous slab reheating furnace, predicting each slab temperature after a plurality of time intervals from the presumed fuel flow rate, and controlling the fuel flow rate for each zone so as to minimize the sum of the differences between the predicted temperatures and corresponding objective temperature rise curves for all the slabs. Alternatively, the method may comprise sensing flow rates of the fuel and air for each zone at time intervals .DELTA.t, calculating the temperature profile within the furnace and then the temperature of each slab at the present time point from the sensed flow rates, repeating the calculations with the calculated slab temperature and any presumed fuel flow rate for each zone to predict the temperature profile within the furnace and each slab temperature after .DELTA.