  We present results on QCD with four dynamical flavors in the temperature
range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice
simulations with Wilson fermions at maximal twist and measured Polyakov loop,
chiral condensate and disconnected susceptibility, on lattices with spacings as
fine as 0.065 fm. For most observables spacing effects are below statistical
errors, which enables us to identify lattice results with continuum estimates.
Our estimate of the pseudocritical temperature compares favorably with
continuum results from staggered and domain wall fermions, confirming that a
dynamical charm does not contribute in the transition region. From the high
temperature behaviour of the disconnected chiral susceptibility we infer the
topological susceptibility, which encodes relevant properties of the QCD axion,
a plausible Dark Matter candidate. The topological susceptibility thus measured
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 seems to approach the DIGA result
from above, a behaviour which would support recent analytic calculations based
on an Instantons-dyons model. These results constrain the mass of a hypothetic
QCD post-inflationary axion, once an assumption concerning the relative
contribution of axions to Dark Matter is made.
