  We consider the simulation of finite temperature QCD with two flavors of
dynamical overlap fermions in order to study the suppression of the axial U(1)
symmetry breaking at the chiral phase transition point. As a preliminary study,
pure gauge simulations are performed to investigate how fixing the topology
affects physical quantities like the topological susceptibility, $\chi_t$, at
finite temperature, showing that it is possible to reconstruct known results
from the fixed topology sector. First results on the degeneracy of meson
correlators in the high temperature QGP sector are shown.
