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 n
umber of colors. We find that both masses decrease at low temperatures, but
only very slightly. We analyze higher order corrections and argue that lar
ge 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 w
ith approximate U(1)(A) symmetry.