Kiln GK3 pushed due to lack of fuel to calciner. Drive belt for calciner coal feeder broke at 4:15 AM. Cntrl Rm Opr received an alarm for coal feeder speed 40 sec after the belt broke. Lack of fuel caused kiln to push (rush hot feed thru kiln) and hot material went to the clinker conveyor system. Diverter gate was opened too late to avoid burning belts.