  We study lattice QCD with $N_f=2$ Wilson fermions at nonzero imaginary
chemical potential and nonzero temperature. We relate the Roberge - Weiss phase
transition to the properties of dyons which are constituents of the KvBLL
calorons. We present numerical evidence that the characteristic features of the
spectral gap of the overlap Dirac operator as function of an angle modifying
the boundary condition are determined by the $Z_3$ sector of the respective
imaginary chemical potential. We then demonstrate that dyon excitations in
thermal configurations could be responsible (in line with perturbative
excitations) for these phenomena.
