In this work, a thermal model for a fused filament fabrication 3D printer extrusion head is proposed. Real-time extruder temperature data were collected and utilized to develop an experiment-based Hammerstein-Wiener model and then linearized to facilitate the development of control techniques later on. The findings of this study will facilitate the development of a data-driven controller to precisely regulate the extruder's temperature in 3D printers, thereby, improving the printing performance and quality.