We evaluate the thermodynamic quantities of the Yang-Mills theory using the Gribov quantization that copes with nonperturbative resummation. The magnetic scale is automatically incorporated in the framework and we find it efficient to stabilize the perturbative expansion of the free energy. In the range of the temperature T=1-2Tc major uncertainty in our results comes from the nonperturbative running coupling that is adopted from the lattice simulation, while the convergence above 2Tc is impressively robust. We also present the corresponding interaction measure (i.e. trace anomaly) up to close to Tc.