  Sterile neutrinos are SU(2) singlets that mix with active neutrinos via a
mass matrix, its diagonalization leads to mass eigenstates that couple via
standard model vertices. We study the cosmological production of heavy
neutrinos via standard model charged and neutral current vertices under a
minimal set of assumptions: i) the mass basis contains a hierarchy of heavy
neutrinos, ii) these have very small mixing angles with the active (flavor)
neutrinos, iii) standard model particles, including light (active-like)
neutrinos are in thermal equilibrium. The same weak interaction processes that
produce active-like neutrinos also produce the heavier species. We introduce
the kinetic equations that describe their production, freeze out and decay and
discuss the various processes that lead to their production in a wide range of
temperatures assessing their feasibility as dark matter candidates. We identify
processes in which finite temperature collective excitations lead to the
production of the heavy species. As a specific example, we consider the
production of heavy neutrinos from pion decay shortly after the QCD crossover
including finite temperature corrections to the pion form factors and mass. We
consider the different decay channels that allow for the production of heavy
neutrinos showing that their frozen distribution functions exhibit effects from
"kinematic entanglement" and argue for their viability as mixed dark matter
candidates. We discuss abundance, phase space density and stability constraints
and argue that heavy neutrinos with lifetime $\tau> 1/H_0$ freeze out of local
thermal equilibrium, and \emph{conjecture} that those with lifetimes $\tau \ll
1/H_0$ may undergo cascade decay into lighter DM candidates and/or inject
non-LTE neutrinos into the cosmic neutrino background. We provide a comparison
with non-resonant production via active-sterile mixing.
