  We examine and point out the importance of a regime of dark matter production
through the freeze-in mechanism that results from a large thermal correction to
a decaying mediator particle mass from hot plasma in the early Universe. We
show that mediator decays to dark matter that are kinematically forbidden at
the usually considered ranges of low temperatures can be generically present at
higher temperatures and actually dominate the overall dark matter production,
thus leading to very distinct solutions from the standard case. We illustrate
these features by considering a dark Higgs portal model where dark matter is
produced via decays of a scalar field with a large thermal mass. We identify
the resulting ranges of parameters that are consistent with the correct dark
matter relic abundance and further apply current and expected future collider,
cosmological, and astrophysical limits.
