Finite temperature QCD with N${}_f$=2+1+1 Wilson twisted mass fermions at physical pion, strange and charm masses

We discuss recent progress in studying Quantum Chromodynamics at finite temperature using N${}_f$=2+1+1 Wilson twisted mass fermions. Particular interest is in QCD symmetries and their breaking and restoration. First, we discuss the behaviour of the η′ meson at finite temperature, which is tightly connected to the axial and chiral symmetries. The results suggest a small decrease of the η′ mass in the pseudo-critical region coming close to the non-anomalous contribution and subsequent growth at large temperatures. Second, we present the first results of lattice simulations of Quantum Chromodynamics with N${}_f$=2+1+1 twisted mass Wilson fermions at physical pion, strange and charm masses. We estimate the chiral pseudo-critical temperatures for different observables. Our preliminary results are consistent with a second order transition in the chiral limit, however other scenarios are not excluded.