  We compute the thermalization of a hidden sector consisting of minicharged
fermions (MCPs) and massless hidden photons in the early Universe. The precise
measurement of the anisotropies of the cosmic microwave background (CMB) by
Planck and the relic abundance of light nuclei produced during big bang
nucleosynthesis (BBN) constrain the amount of dark radiation of this hidden
sector through the effective number of neutrino species, Neff. This study
presents novel and accurate predictions of dark radiation in the strongly and
weakly coupled regime for a wide range of model parameters. We give the value
of Neff for MCP masses between 100 keV and 10 GeV and minicharges in the range
10^(-11)-1. Our results can be used to constrain MCPs with the current data and
they are also a valuable indicator for future experimental searches, should the
hint for dark radiation manifest itself in the next release of Planck's data.
