Fused deposition modeling's (FDM) throughput is limited by process physics as well as practical considerations favoring single-head polymer extrusion. To expedite the thermoplastic additive manufacturing process, we propose a parallelized material deposition process called local viscosity control (LVC) additive manufacturing. LVC prints an entire layer in one step by selectively modulating the viscosity of polymer feedstock in contact with a heated wire mesh. Layers of molten polymer are contact printed, with the relative motion between the wire mechanism and a build plate allowing wetting and surface tension to transfer selectively heated, lower viscosity regions of polymer to a fixed substrate. Experiments demonstrate the viability of this process using a single cell depositing layered polycarbonate pixels. Theoretical analysis shows this process may offer similar capabilities in resolution to conventional FDM with a significantly higher production rate for commonly available input power.