A method for additive manufacturing a part using fused deposition modeling 3D printing technology includes projecting a laser image from one or more laser emitters onto a previously printed bead or beads of thermoplastic material forming a portion of the part, along a tool path for a next bead in a subsequent part layer. The laser image has a width of between about 50% to 75% of a commanded beadwidth of the next bead, and is moved along a tool path that is generally transverse to the width thereof, to thereby selectively irradiate and heat the previously printed thermoplastic material to at least a bonding temperature thereof but below a degradation temperature. A bead of thermoplastic material is extruded from an extrusion head and deposited along the tool path while at least a top surface portion of the irradiated material remains at or above its bonding temperature, so that strong adhesion occurs between part layers.