  Modifications of the $\pi^o\to 2\gamma$ decay amplitude by thermal effects
have already been considered by several authors, leading to quite different
results. I consider in this paper the triangle diagram connecting a neutral
pion to two photons in a constituent quark model, within the real-time
formulation of thermal field theory and study the zero external momentum limit
of this diagram. It appears that this limit is not unique and depends strongly
on the kinematical configuration of the external particles. This non-uniqueness
is shown to explain the contradiction between existing results. I end with some
considerations suggesting that this decay amplitude may be significantly
modified by the resummation of hard thermal loops, due to infrared
singularities.
