  Using the finite temperature quasi-particle random phase approximation
(FTQRPA) on the basis of finite temperature Skyrme-Hartree-Fock + BCS method,
we study $\beta^-$-decay half-lives for even-even neutron magic nuclei with
N=82 in a finite temperature environment. We find that the $\beta^-$-decay
half-life first decreases as the temperature increases for all the nuclei we
study, although the thermal effect is found to be small at temperatures
relevant to r-process nucleosynthesis. Our calculations indicate that the
half-life begins to increase at high temperatures for open shell nuclei. We
discuss this behavior in connection to the pairing phase transition.
