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The recent discovery and characterization of the diversity of the atmospheresof exoplanets and brown dwarfs calls for the development of fast and accurateanalytical models. We quantify the accuracy of the analytical solution derivedin paper I for an irradiated, non-grey atmosphere by comparing it to astate-of-the-art radiative transfer model. Then, using a grid of numericalmodels, we calibrate the different coefficients of our analytical model forirradiated solar-composition atmospheres of giant exoplanets and brown dwarfs.  We show that the so-called Eddington approximation used to solve the angulardependency of the radiation field leads to relative errors of up to 5% on thetemperature profile. We show that for realistic non-grey planetary atmospheres,the presence of a convective zone that extends to optical depths smaller thanunity can lead to changes in the radiative temperature profile on the order of20% or more. When the convective zone is located at deeper levels (such as forstrongly irradiated hot Jupiters), its effect on the radiative atmosphere issmaller. We show that the temperature inversion induced by a strong absorber inthe optical, such as TiO or VO is mainly due to non-grey thermal effectsreducing the ability of the upper atmosphere to cool down rather than anenhanced absorption of the stellar light as previously thought.  Finally, we provide a functional form for the coefficients of our analyticalmodel for solar-composition giant exoplanets and brown dwarfs. This leads tofully analytical pressure-temperature profiles for irradiated atmospheres witha relative accuracy better than 10% for gravities between 2.5m/s^2 and 250m/s^2 and effective temperatures between 100 K and 3000 K. This is a greatimprovement over the commonly used Eddington boundary condition.

A non-grey analytical model for irradiated atmospheres. II: Analytical vs. numerical solutions