[en] It is shown that, as for a Nilsson + pairing model, the extended stability condition of the thermal Hartree-Fock-Bogoliubov (THFB) solution coincides with the one of the thermal RPA (TRPA) solution unless the pairing constant G is too large. As possible extensions of the TRPA equation in alternative ways describing thermal fluctuation effect, the extended TRPA (ETRPA) and the dissipative TRPA (DTRPA) are discussed. Furthermore, the general microscopic framework of the TRPA predicts the saturation and decrease of giant resonance width in high temperature limit, i.e. the fragmentation width Γ_f∝(kT)^(-3(2)) and the spreading width Γ^↓∝(kT)^(-1(2))