  Inhomogeneous pseudoscalar and scalar Bethe-Salpeter equations solved using a
renormalisation-group-improved rainbow-ladder truncation exhibit bound state
poles below and above T_c, the critical temperature for chiral symmetry
restoration. Above T_c the bound state amplitudes are identical, as are the
positions and residues of the pseudoscalar and scalar poles in the vertices. In
the chiral limit the pi^0 -> gamma gamma coupling vanishes at T_c, as do f_pi,
m_sigma, g_{sigma pi pi}. For light current-quark masses the 2-pi decay channel
of the isoscalar-scalar meson remains open until very near T_c, and the widths
of the dominant pion decay modes remain significant in the vicinity of the
crossover.
