In the coronal condition (V_Ae = 1.5, V_Ai = 1, C_si = 0.15, C_se = 0.13 Mm/s) and with $\overline{{\tau }_1}=6.8$, $\overline{{\tau }_2}=2.4$ (corresponding to approximate values of 34 and 12 minutes for τ₁ and τ₂, respectively, at a temperature of about 5 MK), the study considers a wave with a period of 5 min: (a) numerical solution of the dispersion relation from Eq. (19) for frequencies (phase speed) normalized by the internal acoustic frequency (acoustic speed) (ω_r/ω_si ≡ v_ph/C_si) of the fast sausage fundamental mode without (solid blue line) and with (solid black line) consideration of the thermal misbalance effect, as well as the numerical solution of the dispersion relation from Eq. (27) for the fast kink fundamental mode (m = 1) without (dashed blue line) and with (dashed black line) consideration of the thermal misbalance effect versus the normalized longitudinal wavenumber (kR). (b) Damping rate to frequency ratio (−γ/ω_r) of fundamental states of the fast sausage (solid line) and kink (dashed line) modes with consideration of the thermal misbalance effect versus the normalized longitudinal wavenumber (kR).