Additive Manufacturing Techniques such as Fused Filament Fabrication (FFF) produce 3D parts with complex geometries directly from a computer model without the need of using molds and tools, by gradually depositing material(s), usually in layers. Due to the rapid growth of these techniques, researchers have been increasingly interested in the availability of strategies, models or data that may assist process optimization. In fact, 3D printed parts often exhibit limited mechanical performance, which is usually the result of poor bonding between adjacent filaments. In turn, the latter is influenced by the temperature field history during deposition. This study aims at evaluating the influence of the phase change from the melt to the solid state undergone by semi-crystalline polymers such as Polylactic Acid (PLA), on the heat transfer during the deposition stage. The energy equation considering solidification is solved analytically and then inserted into a MatLab® code to model cooling in FFF. The deposition and cooling of simple geometries is studied first, in order to assess the differences in cooling of amorphous and semi-crystalline polymers. Acrylonitrile Butadiene Styrene (ABS) was taken as representing an amorphous material. Then, the deposition and cooling of a realistic 3D part is investigated, and the influence of the build orientation is discussed.