  We study the temperature dependence of the eta and eta' meson masses within
the framework of U(3)_L x U(3)_R chiral perturbation theory, up to
next-to-leading order in a simultaneous expansion in momenta, quark masses and
number of colours. We find that both masses decrease at low temperatures, but
only very slightly. We analyze higher order corrections and argue that large
N_c suggests a discontinuous drop of M_eta' at the critical temperature of
deconfinement T_c, consistent with a first order transition to a phase with
approximate U(1)_A symmetry.
