A liquefier assembly for use in an additive manufacturing system, which includes a rigid member having a gap, a liquefier tube operably disposed in the gap, one or more heater assemblies disposed in the gap in contact with the liquefier tube, and configured to heat the liquefier tube in a zone-by-zone manner, preferably one or more thermal resistors disposed in the gap between the rigid member and the heater assemblies, and preferably one or more sensors configured to operably measure pressure within the liquefier tube. The one or more heater assemblies may be operated to provide dynamic heat flow control.