  The multipole response of nuclei at temperatures T=0-2 MeV is studied using a
self-consistent finite-temperature RPA (random phase approximation) based on
relativistic energy density functionals. Illustrative calculations are
performed for the isoscalar monopole and isovector dipole modes and, in
particular, the evolution of low-energy excitations with temperature is
analyzed, including the modification of pygmy structures. Both for the monopole
and dipole modes, in the temperature range T=1-2 MeV additional transition
strength appears at low energies because of thermal unblocking of
single-particle orbitals close to the Fermi level. A concentration of dipole
strength around 10 MeV excitation energy is predicted in $^{60,62}$Ni, where no
low-energy excitations occur at zero temperature. The principal effect of
finite temperature on low-energy strength that is already present at zero
temperature, e.g. in $^{68}$Ni and $^{132}$Sn, is the spreading of this
structure to even lower energy and the appearance of states that correspond to
thermally unblocked transitions.
