Extrusion bioprinting is a popular method for fabricating tissue engineering scaffolds because of its potential to rapidly produce complex, bioactive or cell-laden scaffolds. However, due to the relatively high viscosity required to maintain shape fidelity during printing, many extrusion-based inks lack the ability to achieve precise structures at scales lower than hundreds of micrometers. In this work, we present a novel poly(N-isopropylacrylamide) (PNIPAAm)-based ink and poloxamer support bath system that produces precise, multi-layered structures on the tens of micrometers scale. The support bath maintains the structure of the ink in a hydrated, heated environment ideal for cell culture, while the ink undergoes rapid thermogelation followed by a spontaneous covalent crosslinking reaction. Through the combination of the PNIPAAm-based ink and poloxamer bath, this system was able to produce hydrogel scaffolds with uniform fibers possessing diameters tunable from 80 to 200 μm. A framework of relationships between several important printing factors involved in maintaining support and thermogelation was also elucidated. As a whole, this work demonstrates the ability to produce precise, acellular and cell-laden PNIPAAm-based scaffolds at high-resolution and contributes to the growing body of research surrounding the printability of extrusion-based bioinks with support baths.