  One of the remarkable interaction effects on topological insulators is the
reduction of topological classification in free-fermion systems. We address
this issue in a bilayer honeycomb lattice model by taking into account
temperature effects on the reduction. Our analysis, based on the real-space
dynamical mean field theory, elucidates the following results. (i) Even when
the reduction occurs, the winding number defined by the Green's function can
take a nontrivial value at zero temperature. (ii) The winding number taking the
nontrivial value becomes consistent with the absence of gapless edge modes due
to Mott behaviors emerging only at the edges. (iii) Temperature effects can
restore the gapless edge modes, provided that the energy scale of interactions
is smaller than the bulk gap. In addition, we observe the topological edge Mott
behavior only in some finite temperature region.
