  We investigate the topological properties of unquenched $QCD$ on the basis of
numerical results of simulations at fixed topological charge, recently reported
by Borsanyi et al.. We demonstrate that their results for the mean value of the
chiral condensate at fixed topological charge are inconsistent with the
analytical prediction of the large volume expansion around the saddle point,
and argue that the most plausible explanation for the failure of the saddle
point expansion is a vacuum energy density $\theta$-independent at high
temperatures, but surprisingly not too high $(T\sim 2T_c)$, a result which
would imply a vanishing topological susceptibility, and the absence of all
physical effects of the $U(1)$ axial anomaly at these temperatures. We also
show that under a general assumption concerning the high temperature phase of
$QCD$, where the $SU(N_f)_A$ symmetry is restored, the analytical prediction
for the chiral condensate at fixed topological charge is in very good agreement
with the numerical results of Borsanyi et al., all effects of the axial anomaly
should disappear, the topological susceptibility and all the
$\theta$-derivatives of the vacuum energy density vanish and the theory becomes
$\theta$-independent at any $T>T_c$ in the infinite volume limit.
