ABSTRACT Light emission in the first hours and days following core-collapse supernovae (SNe) is dominated by the escape of photons from the expanding shock-heated envelope. In a preceding paper, Paper I, we provided a simple analytic description of the time-dependent luminosity, L, and colour temperature, Tcol, valid up to H recombination (T ≈ 0.7 eV), for explosions of red supergiants with convective polytropic envelopes without significant circumstellar medium (CSM). The analytic description was calibrated against ‘grey’ (frequency-independent) photon diffusion numeric calculations. Here, we present the results of a large set of 1D multigroup (frequency-dependent) calculations, for a wide range of progenitor parameters (mass, radius, core/envelope mass ratios, metalicity) and explosion energies, using opacity tables that we constructed (and made publicly available), including the contributions of bound–bound and bound–free transitions. We provide an analytic description of the small, ${\simeq}10\ \hbox{per cent}$ deviations of the spectrum from blackbody at low frequencies, hν < 3Tcol, and an improved (over Paper I) description of ‘line dampening’ for hν > 3Tcol. We show that the effects of deviations from initial polytropic density distribution are small, and so are the effects of ‘expansion opacity’ and deviations from LTE ionization and excitation (within our model assumptions). A recent study of a large set of type II SN observations finds that our model accounts well for the early multiband data of more than 50 per cent of observed SNe (the others are likely affected by thick CSM), enabling the inference of progenitor properties, explosion velocity, and relative extinction.