Additive manufacturing (AM) has drawn interest from fields ranging from aerospace to regenerative medicine to metamaterials. Using AM, specimens with complex internal geometries and structures can be manufactured. Despite the advantages and interest, broader use of AM is limited by poor mechanical properties, lack of reliability, and lack of expertise. To better understand Material Extrusion (MatEx) AM, a simulation was developed that describes temperature throughout a build. At benchtop (FFF) scales, short times over Tg were reported, indicating limited opportunity for interlayer diffusion. Additionally, maxima in cooling rates were observed at print speeds of 10-30 mm/s, which may have implications for residual stress formation. At larger (BAAM) scales, much longer times of Tg were observed, which can lead to continued flow of extruded material and warping of the printed structure. The effects of material and processing parameters were investigated at both scales, and different trends in thermal behavior were observed at the small and large scale. The metrics of thermal behavior that were monitored include cooling rate, time to Tg, steady state temperature, and equivalent isothermal weld time, which are related to the mechanical performance of MatEx structures. These results indicate that designing MatEx materials and processes in concert will lead to improved structure performance, and give preliminary guidance in development of design rules.