The high temperature phases of BiFeO3 have courted much controversy with many conflicting structural models reported, in particular for the paraelectric β-phase. High temperature powder neutron diffraction (PND) experiments indicate that the ferroelectric (R3c) α-phase transforms to the paraelectric β-phase at approximately 820 °C via a first order phase transition. We demonstrate that this phase is unambiguously orthorhombic, adopting the GdFeO3 structure-type with a space group Pbnm. On further heating BiFeO3 undergoes another first order phase transition (β-γ) at approximately 930 °C which is marked by a discontinuous decrease in cell volume consistent with an insulator-metal transition. Close inspection of the PND data show no evidence of any symmetry change, with the postulated γ-phase remaining orthorhombic Pbnm. In addition we present PND and impedance spectroscopy data for BiFeO3 which suggest that the so-called ‘Połomska’ transition observed by some authors at approximately 185 °C is not intrinsic.