There's plenty of proof in academic literature. FePO4 is quite stable because of the quirks in iron's valance up to about 500C. But the combination of of lithium skews the valance effects at high temperatures to start losing oxygen at 250C.
Please review the following literature for more information:
C. Delacourt, P. Poizot, J-.M. Tarascon, and C. Masquelier, Nat Mater., 4, 254 (2005).
J.L Dodd, R. Yazami, and B. Fultz, Electrochem. Solid-State Let., 9, A151 (2006).
G. Chen, .XSong, and T. J. Richardson, J. Electrochem. Soc,. 154, 4627 (2007).
Phosphate will decompose into phosphate ions and oxygen given enough energy. The energy of the P--O bond is greater than Co--O but ultimately means that LFP batteries are also self-oxidizing but less so than lithium cobalt oxide