Neutron diffraction, X-ray absorption spectroscopy (XAS), and Raman spectroscopy measurements of the quaternary perovskite phase Ba2NaMoO5.5 have been performed in this work. The cubic crystal structure in space group Fm3¯ m has been refined using the Rietveld method. X-ray absorption near-edge structure spectroscopy (XANES) measurements at the Mo K-edge have confirmed the hexavalent state of molybdenum. The local structure of the molybdenum octahedra has been studied in detail using extended X-ray absorption fine structure (EXAFS) spectroscopy. The Mo-O and Mo-Ba distances have been compared to the neutron diffraction data with good agreement. The coefficient of thermal expansion measured in the temperature range of 303-923 K, using high temperature X-ray diffraction (HT-XRD) (αV = 55.8 × 10-6 K), has been determined to be ∼2 times higher than that of the barium molybdates BaMoO3 and BaMoO4. Moreover, no phase transition nor melting have been observed, neither by HT-XRD nor Raman spectroscopy nor differential scanning calorimetry, up to 1473 K. Furthermore, the standard enthalpy of formation (ΔfHm°) for Ba2NaMoO5.5(cr) has been determined to be -(2524.75 ± 4.15) kJ mol-1 at 298.15 K, using solution calorimetry. Finally, the margin for safe operation of sodium-cooled fast reactors (SFRs) has been assessed by calculating the threshold oxygen potential needed, in liquid sodium, to form the quaternary compound, following an interaction between irradiated mixed oxide (U,Pu)O2 fuel and sodium coolant.