An additive manufacturing apparatus, and corresponding method, determine a mass (or volume) output flow rate of extrudate used in three-dimensional (3D) printing, and such determination is insensitive to rheological properties of a material of the extrudate being printed. A thermal energy balance on a liquefying extrusion head enables a load on a heater, used to heat the extrusion head, to be related to the output flow rate of extrudate. Based on the thermal energy balance, the output flow rate may be determined based on a duty cycle of the heater. The output flow rate may be employed to affect the 3D printing to prevent over- or under-extrusion of the extrudate and to identify a fault condition.