  We present results on QCD with four dynamical flavors in the temperature
range $0.9 \lesssim T/T_c \lesssim 2$. We have performed lattice simulations
with Wilson fermions at maximal twist and measured the topological charge with
gluonic and fermionic methods. The topological charge distribution is studied
by means of its cumulants, which encode relevant properties of the QCD axion, a
plausible Dark Matter candidate. The topological susceptibility measured with
the fermionic method exhibits a power-law decay for $T/T_c \gtrsim 2$, with an
exponent close to the one predicted by the Dilute Instanton Gas Approximation
(DIGA). Close to $T_c$ the temperature dependent effective exponent approaches
the DIGA result from above, in agreement with recent analytic calculations.
These results constrain the axion window, once an assumption on the fraction of
axions contributing to Dark Matter is made.
