We observe that photon cooling after big bang nucleosynthesis but before recombination can remove the conflict between the observed and theoretically predicted value of the primordial abundance of ^{7}Li. Such cooling is ordinarily difficult to achieve. However, the recent realization that dark matter axions form a Bose-Einstein condensate provides a possible mechanism because the much colder axions may reach thermal contact with the photons. This proposal predicts a high effective number of neutrinos as measured by the cosmic microwave anisotropy spectrum.