  We examine the axial U(1) symmetry near and above the finite temperature
phase transition in two-flavor QCD using lattice QCD simulations. Although the
axial U(1) symmetry is always violated by quantization, (i.e.) the chiral
anomaly, the correlation functions may manifest effective restoration of the
symmetry in the high temperature phase. We explicitly study this possibility by
calculating the meson correlators as well as the Dirac operator spectral
density near the critical point. Our numerical simulations are performed on a
$16^3\times 8$ lattice with two flavors of dynamical quarks represented by the
overlap fermion formalism. Chiral symmetry and its violation due to the axial
anomaly is manifestly realized with this formulation, which is a prerequisite
for the study of the effective restoration of the axial U(1) symmetry. In order
to avoid discontinuity in the gauge configuration space, which occurs for the
exactly chiral lattice fermions, the simulation is confined in a fixed
topological sector. It induces finite volume effect, which is well described by
a formula based on the Fourier transform from the $\theta$-vacua. We confirm
this formula at finite temperature by calculating the topological
susceptibility in the quenched theory. Our two flavor simulations show
degeneracy of the meson correlators and a gap in the Dirac operator spectral
density, which implies that the axial U(1) symmetry is effectively restored in
the chirally symmetric phase.
