We report a temperature-dependent high-resolution x-ray diffraction investigation of 200-nm epitaxial BiFeO3 thin films grown on (001) SrTiO3. We find that BiFeO3 undergoes two high-temperature transitions: a first-order alpha-beta phase transition between 745 and 780 degrees C and a more diffuse transition toward the gamma phase at 860 degrees C. Reciprocal space maps reveal that thin films remain monoclinic crossing the alpha-beta phase transition. Linear extrapolation of the in-plane lattice parameters to higher temperatures appears to rule out cubic symmetry for the gamma phase.