We report on the molecular origin of poly-(pentamethylene 2,5-furanoate)'s particular physical properties. From the structural point of view, we found that this polymer can develop crystallinity when stored under room conditions for months. On the other hand, we used broadband dielectric spectroscopy measurements to analyze in great detail the local and segmental molecular dynamics of the material subjected to several thermal treatments. In this way, we evidenced that the molecular dynamics are sensitive to thermal history over a broad temperature range. This behavior has been attributed to possible interchain interactions detected via infrared spectroscopy and rheology measurements in the noncrystallized polymer.