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Thermal fluctuations of quasiparticle number are included making use of thesecondary Bogolyubov's transformation, which turns quasiparticles operatorsinto modified-quasiparticle ones. This restores the unitarity relation for thegeneralized single-particle density operator, which is violated within theHartree-Fock-Bogolyubov (HFB) theory at finite temperature. The resultingtheory is called the modified HFB (MHFB) theory, whose limit of a constantpairing interaction yields the modified BCS (MBCS) theory. Within the MBCStheory, the pairing gap never collapses at finite temperature T as it doeswithin the BCS theory, but decreases monotonously with increasing T. It isdemonstrated that this non-vanishing thermal pairing is the reason why thewidth of the giant dipole resonance (GDR) does not increase with T up to Taround 1 MeV. At higher T, when the thermal pairing is small, the GDR widthstarts to increase with T. The calculations within the phonon-damping modelyield the results in good agreement with the most recent experimentalsystematic for the GDR width as a function of T. A similar effect, which causesa small GDR width at low T, is also seen after thermal pairing is included inthe thermal fluctuation model.Comment: Invited lecture at the Predeal international summer school in nuclear  physics on ``Collective motion and phase transitions in nuclear systems'', 28  August - 9 September, 2006, Predeal, Romania; 18 pages, 3 figures; to be  published by World Scientific in the proceedings of this schoo

SUPERFLUID-NORMAL PHASE TRANSITION IN FINITE SYSTEMS AND ITS EFFECT ON DAMPING OF HOT GIANT RESONANCES