Methods for substantially improving the stability of a melting furnace system including bushings and cooling apparatus for converting molten mineral material to continuous fibers is disclosed. Apparatus and methods for maintaining the molten material throughput and the electrical power load on fiberizing bushings substantially constant are disclosed. The orifice plate, with or without tips or nozzles, is subjected to a more rapid rate of heat removal after the bushing breaks out than it did while the bushing was in a desired fiberizing mode. Apparatus for blowing cooling air upward onto the orifice plate during the time the bushing is breaking out and/or hanging to provide additional cooling is disclosed along with optional additional or alternative apparatus to use for optional additional or alternative cooling is also disclosed.