The Na-ion battery technology appears as a reliable, sustainable and environmentally friendly alternative to the Li-ion one, especially for stationary energy storage. As for the Li-ion technology, safety aspect is of high importance to ensure large-scale development. In this work, we studied the thermal stability and decomposition mechanisms of carbon-coated Na3V2(PO4)2F3 and two fluorine-rich phases belonging to the solid-solution Na3V3+2-yV4+y(PO4)2F3-yOy (y = 0.07 and y = 0.12), that family of compounds being often considered among the most promising positive electrode materials for Na-ion batteries. This study shows the good thermal stability of these polyanionic materials and reveals that a low O2- for F- substitution has a very limited effect on the thermal stability of fully re-intercalated materials recovered in the discharged state of the battery, whereas it has a beneficial impact for highly de-intercalated ones, obtained by in-depth charges. Furthermore, whatever the state of charge and the oxygen content in NaxV2(PO4)2F3-yOy (1<=x<=3 and y = 0, 0.07 and 0.12), the thermal degradation leads, quite unexpectedly, to the formation of crystalline Na3V3+2(PO4)2F3 in addition to an amorphous phase. The fluorination of the partially oxygen for fluorine substituted material was clearly demonstrated by X-ray diffraction (XRD) and solid state nuclear magnetic resonance spectroscopy (NMR) on materials recovered after differential scanning calorimetry (DSC) analyses. The formation of a fully sodiated crystalline phase from the thermal degradation of the material obtained in charged states of the battery, with or without presence of electrolyte, was never reported before.