  The relativistic and nonrelativistic finite temperature proton-neutron
quasiparticle random phase approximation (FT-PNQRPA) methods are developed to
study the interplay of the pairing and temperature effects on the Gamow-Teller
excitations in open-shell nuclei, as well as to explore the model dependence of
the results by using two rather different frameworks for effective nuclear
interactions. The Skyrme-type functional SkM* is employed in the
nonrelativistic framework, while the density-dependent meson-exchange
interaction DD-ME2 is implemented in the relativistic approach. Both the
isoscalar and isovector pairing interactions are taken into account within the
FT-PNQRPA. Model calculations show that below the critical temperatures the
Gamow-Teller excitations display a sensitivity to both the finite temperature
and pairing effects, and this demonstrates the necessity for implementing both
in the theoretical framework. The established FT-PNQRPA opens perspectives for
the future complete and consistent description of astrophysically relevant weak
interaction processes in nuclei at finite temperature such as $\beta$-decays,
electron capture, and neutrino-nucleus reactions.
