  A recent experiment has observed the antiferromagnetic interaction between
the ground state $^1S_0$ and the metastable state $^3P_0$ of $^{171}$Yb atoms,
which are fermionic. This observation combined with the use of state-dependent
optical lattices allows for quantum simulation of the Kondo model. We propose
that in this Kondo simulator the anomalous temperature dependence of transport,
namely the Kondo effect, can be detected through quench dynamics triggered by
the shift of a trap potential. For this purpose, we improve the numerical
efficiency of the minimally entangled typical thermal states (METTS) algorithm
by applying additional Trotter gates. Using the improved METTS algorithm, we
compute the quench dynamics of the one-dimensional Kondo model at finite
temperatures quasi-exactly. We find that the center-of-mass motion exhibits a
logarithmic suppression with decreasing the temperature, which is a
characteristic feature of the Kondo effect.
