A carriageless print head assembly, for use in extrusion-based additive construction is disclosed. The carriageless print head features a cold end equipped with one or more timing belt attachment slots and bores for receiving bearings to achieve linear motion. The carriageless print head may be optionally equipped with some combination of an air conduit for cooling the top layer of the constructed product, a fluid channel for aiding in the regulation of the temperature of the print head cold end, and a thermal monitor for monitoring the temperature of the cold end of the print head. A computer-mediated method of monitoring the cold end of the print head to limit jams due to overheating is also disclosed.