  We present the results on topological susceptibility and chiral observables
in $N_f=2+1+1$ QCD for temperature range $120<T<600$ MeV. The lattice
simulations are performed with Wilson twisted mass fermions at physical pion,
strange and charm masses. In high-$T$ region $T\gtrsim 300$ MeV the chiral
observables are shown to follow leading order Griffith analyticity, and the
topological susceptibility follows a power-law decay as in the instanton dilute
gas models. The measured topological susceptibility is used to estimate the
mass of QCD axion. The resulting axion mass constraints are in agreement with
our previous studies at higher pion masses.
