  The approach in a theory of collective excitations in hot nuclei exploring
the formalism of thermo field dynamics and the model Hamiltonian consisting of
a mean field, the BCS paring interaction and long-range particle-hole effective
forces is reexamined. In contrast with earlier studies it is found that a wave
function of a thermal phonon is depended not only on the Fermi-Dirac thermal
occupation numbers of Bogoliubov quasiparticles consisting the phonon but on
the Bose thermal occupation numbers of the phonon as well. This strongly
affects a thermal phonon couplings due to renormalizing of a phonon-phonon
interaction and enlarging the number of thermal two-phonon configurations
coupled with one-phonon ones. Moreover, it is shown that the formulation of the
double tilde conjugation rule for fermions proposed by I.Ojima is more
appropriate in the context of the present study than the original one by
H.Umezawa and coworkers.
