  We consider relatively heavy neutrinos $\nu_H$, mostly contributing to a
sterile state $\nu_s$, with mass in the range 10 MeV $\lesssim m_s \lesssim
m_{\pi} \sim 135$ MeV, which are thermally produced in the early universe in
collisional processes involving active neutrinos, and freezing out after the
QCD phase transition. If these neutrinos decay after the active neutrino
decoupling, they generate extra neutrino radiation, but also contribute to
entropy production. Thus, they alter the value of the effective number of
neutrino species $N_{\rm eff}$ as for instance measured by the cosmic microwave
background (CMB), as well as affect primordial nucleosynthesis (BBN), notably
${}^4$He production. We provide a detailed account of the solution of the
relevant Boltzmann equations. We also identify the parameter space allowed by
current Planck satellite data and forecast the parameter space probed by future
Stage-4 ground-based CMB observations, expected to match or surpass BBN
sensitivity.
