We report the temperature-dependent Raman and dielectric spectroscopy of chemically synthesized BiFeO3 nanoparticles (average size similar to 50-60 nm). The Raman spectra (90-700 K) show two sets of transitions in the lowest Raman E mode, associated with Bi-O bond motion situated in close proximity to the spin reorientation transitions reported for BiFeO3, thereby indicating the existence of possible coupling between magnons and phonons for particle size below the helical order parameter (62 nm). These transitions are slightly shifted in temperature in comparison to the bulk single crystals. We also observe a step-like behavior in Raman peak position around the Neel temperature, suggesting that the phonons are influenced by the magnetic ordering in nanosized BiFeO3. The heat-flow measurements show two sharp endothermic peaks at 1094 and 1223 K representing rhombohedral to orthorhombic or monoclinic transition followed by transition into the cubic phase above 1200K. The low temperature (20-325 K), frequency-dependent (1-10(6) Hz) dielectric constant and loss tangent measurements show that the loss tangent (similar to 10(-3)) and ac conductivity values (similar to 10(-8) Ohm(-1)-cm(-1)) are orders of magnitude lower than the reported values for BiFeO3 ceramics, indicating high levels of ionic purity of our samples. The real part of the permittivity shows a slight reduction in its value (similar to 30) in comparison to the bulk single crystals. Similar to the Stokes Raman shift, its temperature-dependent dielectric constant also shows four weak anomalies at similar to 85, 168, 205, and 230 K situated in close proximity to the spin reorientation transitions, indicating magnetoelectric coupling.