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Using the numerical renormalization group method, the effect due to a Kondoimpurity in an $s$-wave superconductor is examined at finite temperature ($T$).The $T$-behaviors of the spectral function and the magnetic moment at theimpurity site are calculated. At $T$=0, the spin due to the impurity is insinglet state when the ratio between the Kondo temperature $T_k$ and thesuperconducting gap $\Delta$ is larger than 0.26. Otherwise, the spin of theimpurity is in a doublet state. We show that the separation of the doubleYu-Shiba-Rusinov peaks in the spectral function shrinks as $T$ increases if$T_k/\Delta<0.26$ while it is expanding if $T_k/\Delta>0.26$ and $\Delta$remains to be a constant. These features could be measured by experiments andthus provide a unique way to determine whether the spin of the single Kondoimpurity is in singlet or doublet state at zero temperature.

Temperature-dependent spectral function of a Kondo impurity in an $s$-wave superconductor