Self-consistent theory frameworks have been introduced for description of excitations in nuclei at finite temperature, based on energy density functionals formulated using i) relativistic mean field Lagrangian with density dependent meson-nucleon vertex functions, and ii) Skyrme-type functionals. Finite temperature random phase approximation (FTRPA) has been employed in description of multipole excitations and charge-exchange modes. It is shown that in the temperature range T = 1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. Within the finite temperature Hartree-Fock+RPA based on Skyrme functionals, the electron capture cross sections have been studied for target nuclei at temperatures relevant in modeling the supernova evolution.