This work is devoted to the thermodynamics of high-temperature dense hydrogenplasmas in the pressure region between 10-1 and 102 Mbar. Inparticular, we present for this region results of extensive calculations basedon a recently developed path integral Monte Carlo scheme (direct PIMC). Thismethod allows for a correct treatment of the thermodynamic properties of hotdense Coulomb systems. Calculations were performed in a broad region of thenon-ideality parameter Γ≲3 and degeneracy parameterneΛ3≲10. We give a comparison with a few availableresults from other path integral calculations (restricted PIMC) and withanalytical calculations based on Padé approximations for strongly ionizedplasmas. Good agreement between the results obtained from the threeindependent methods is found.