Progresses on high-temperature QCD: Equation of State and energy-momentum tensor

We present first non-perturbative results for the renormalization constants of the QCD energy-momentum tensor, based on the framework of thermal QCD with shifted and twisted (for quarks only) boundary conditions in the compact direction. We also show preliminary results for the entropy density obtained with the very same numerical strategy. This opens the way to the determination of the QCD Equation of State up to very high temperatures.