The crystal structure of Aurivillius phase ferroelectric Bi2WO6 has been studied in detail as a function of temperature by using high-resolution powder neutron diffraction. In agreement with an earlier study, a transition from space group P2(1)ab to B2cb occurs at about 660 degrees C. This transition corresponds to the loss of one octahedral tilt mode within the perovskite-like WO4 layer of the structure. A second, reconstructive, phase transition occurs around 960 degrees C, corresponding to the ferroelectric Curie point; in contrast to previous suggestions, the structure of this high-temperature phase contains layers of stoichiometry WO4, with WO6 octahedra sharing edges and corners, and with the fluorite-like Bi2O2 layers remaining essentially unchanged. This structure is closely related to that of the ambient temperature phase of lanthanide-doped derivatives, for example, Bi0.7Yb1.3WO6 recently reported. This phase-transition behaviour is in stark contrast to that of other members of the Aurivillius family, such as SrBi2Ta2O9 and Bi4Ti3O12, which retain the archetypal Aurivillius connectivity at all temperatures.