How pi0 ---> gamma gamma changes with temperature

At zero temperature, in the chiral limit the amplitude for pi0 to decay into two photons is directly related to the coefficient of the axial anomaly. At any nonzero temperature, this direct relationship is lost: while the coefficient of the axial anomaly is independent of temperature, in a thermal bath the anomalous Ward identities do not uniquely constrain the amplitude for pi0 -> gamma gamma. Explicit calculation shows that to lowest order about zero temperature, this amplitude decreases.