In the coronal condition and $\overline{{\tau }_1}=6.8$, $\overline{{\tau }_2}=2.4$: (a) numerical solution of the dispersion relation Eq. (18), computed by MATLAB, for the frequency (phase speed) normalized by the internal acoustic frequency (acoustic speed) (ℜ𝔢(ω)/ω_si ≡ v_ph/C_si) of the fundamental slow sausage mode without consideration of the thermal misbalance effect (unaffected) (solid blue line) and with consideration of the thermal misbalance effect (affected) (solid black line), as well as the fundamental slow kink mode unaffected (dashed blue line) and affected (dashed black line) by the thermal misbalance versus the normalized longitudinal wavenumber (kR). (b) Damping rate to the frequency ratio (−γ/ω_r) of fundamental states of the affected slow sausage (solid line) and kink (dashed line) modes by the thermal misbalance versus the normalized longitudinal wavenumber (kR). (c) Damping time to the wave period ratio (τ_d/P) of the affected slow sausage (solid line) and kink (dashed line) modes by the thermal misbalance versus the normalized longitudinal wavenumber (kR). For comparison, the analytical results obtained by Eqs. (25, 32) are shown by the black and blue solid curves in panels d, e, f.