  We describe how the thermal counterpart of a vacuum two-point function may be
obtained in the real time formalism in a simple way by using directly the
$2\times 2$ matrices that different elements acquire in this formalism. Using
this procedure we calculate the analytic (single component) thermal amplitude
for the pion pole term in the ensemble average of two axial-vector currents to
two loops in chiral perturbation theory. The general expressions obtained for
the effective mass and decay constants of the pion are evaluated in the chiral
and the nonrelativistic limits. We also investigate the effect of massive
states on these effective parameters.
