  We study temperature dependence of the topological susceptibility with the
$N_{f}=2+1$ flavors Wilson fermion. We have two major interests in this paper.
One is a comparison of gluonic and fermionic definitions of the topological
susceptibility. Two definitions are related by the chiral Ward-Takahashi
identity but their coincidence is highly non-trivial for the Wilson fermion. By
applying the gradient flow both for the gauge and quark fields we find a good
agreement of these two measurements. The other is a verification of a
prediction of the dilute instanton gas approximation at low temperature region
$T_{pc}< T<1.5T_{pc}$, for which we confirm the prediction that the topological
susceptibility decays with power $\chi_{t}\propto(T/T_{pc})^{-8}$ for three
flavors QCD.
