Pair production in a plane wave due to a thermal background

Ever since Schwinger's publication [J. Schwinger, Phys. Rev. 82, 664 (1951)], the maxim that there can be no pair creation from vacuum in a plane wave has been often cited. We put forward an analysis showing that in any real situation, where thermal effects are present, in a single plane-wave field, even in the limit of zero frequency (a constant crossed field), pair creation can indeed occur. Interestingly, we find that the pair-production rate depends non-perturbatively on both the temperature and the amplitude of the constant crossed field.