We report our study on the properties of the topological structures present in the QCD medium around the critical temperature $T_c$. We use dynamical domain wall fermion configurations on lattices of size $32^3 \times 8$ to detect the topological structures through the zero and near-zero modes of the overlap operator. We show that the properties of the zero modes of the QCD Dirac operator agree well with that of calorons with non-trivial holonomy. We also show how the zero modes move around when changing the fermionic boundary conditions, and how the locality of the solutions also depends on the boundary conditions. This supports the presence of instanton-dyons in the hot QCD medium around $T_c$, where the distance between dyons control the shape and extent of the zero modes.