In controlling a slab reheat furnace, the average temperature of each slab in a zone, is predicted as a function of the radiation heat source temperature in the zone, and the thermal properties, dimensions, location, velocity, and past thermal history of the slabs. The predicted slab temperatures are compared with a range of desired slab temperatures and the slab requiring the greatest time to be heated to its desired temperature is identified. The furnace is controlled in such a manner that the identified slab will be heated to the desired temperature. Slabs likely to be overheated are identified and, if a predetermined temperature limit is to be exceeded, the furnace is controlled to prevent further heating of the slabs. Gas temperatures throughout the zone are predicted based upon only one sensed temperature in the zone.