Disclosed are systems and methods for forming glass sheets. Methods and systems are provided that comprise a refractory body configured to receive glass-based material and means for transmitting energy to selectively heat at least a portion of the refractory body through the glass-based material. In one aspect, the energy transmitted is of a selected frequency that is not fully absorbed by the glass-based material and is at least partially absorbed by the refractory body. The energy can be transmitted by a laser beam array, a scanning laser beam, a microwave generator, a radio frequency generator, or other means.