  A microscopic approach to the proton-neutron nuclear response is formulated
in the finite-temperature relativistic nuclear field theory framework. The
approach is based on the meson-nucleon Lagrangian of quantum hadrodynamics and
advances the relativistic field theory for spin-isospin response beyond the
finite-temperature random phase approximation. The dynamical contribution to
the in-medium proton-neutron interaction amplitude is described in a
parameter-free way by the coupling between the single nucleons and
strongly-correlated particle-hole excitations (phonons) within the newly
developed finite-temperature formalism. In this framework we investigate
temperature dependence of the Gamow-Teller and spin dipole resonances in the
closed-shell nuclei $^{48}$Ca, $^{78}$Ni, and $^{132}$Sn. Broader impacts of
their temperature dependence are illustrated for the associated beta decay
rates and lifetimes of $^{78}$Ni and $^{132}$Sn in hot astrophysical
environments. We found a remarkable sensitivity of the beta decay rates to the
enhanced low-energy spin-isospin strength at finite temperature, in particular,
to the contribution of the first-forbidden transitions.
