  The temperature-dependent electronic structures of heavy fermion compound
CeB$_{6}$ are investigated thoroughly by means of the combination of density
functional theory and single-site dynamical mean-field theory. The band
structure, density of states, and 4$f$ valence state fluctuation of CeB$_{6}$
are calculated in a broad temperature range of 10 $\sim$ 120 K. Overall, the
4$f$ electrons remain incoherent, approximately irrespective of the
temperature. However, we find that these observables exhibit some unusual
features near 20 K. In addition, the evolution of 4$f$ orbital occupancy, total
angular momentum, and total energy with respect to temperature shows apparent
singularity around 20 K. We believe that these tantalizing characteristics are
probably related to a "hidden" electronic transition.
