In the core-accretion formation scenario of gas giants, most of the gas accreting onto a planet is processed through an accretion shock. In this series of papers we study this shock since it is key in setting the forming planets structure and thus its post-formation luminosity, with dramatic observational consequences. We perform one-dimensional grey radiation-hydrodynamical simulations with non-equilibrium (two-temperature) radiation transport and up-to-date opacities. We survey the parameter space of accretion rate, planet mass, and planet radius and obtain post-shock temperatures, pressures, and entropies, as well as global radiation efficiencies. We find that usually, the shock temperature T_shock is given by the free-streaming limit. At low temperatures the dust opacity can make the shock hotter but not significantly. We corroborate this with an original semi-analytical derivation of T_shock . We also estimate the change in luminosity between the shock and the nebula. Neither T_shock nor the luminosity profile depend directly on the optical depth between the shock and the nebula. Rather, T_shock depends on the immediate pre-shock opacity, and the luminosity change on the equation of state (EOS). We find quite high immediate post-shock entropies (S ~ 13-20 kB/mH), which makes it seem unlikely that the shock can cool the planet. The global radiation efficiencies are high (eta^phys > 97%) but the remainder of the total incoming energy, which is brought into the planet, exceeds the internal luminosity of classical cold starts by orders of magnitude. Overall, these findings suggest that warm or hot starts are more plausible.
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