  A very simple production mechanism of feebly interacting dark matter (DM)
that rarely annihilates is thermal production, which predicts the DM mass
around eV. This has been widely known as the hot DM scenario. Despite there are
several observational hints from background lights suggesting a DM in this mass
range, the hot DM scenario has been considered strongly in tension with the
structure formation of our Universe because the free-streaming length of the DM
produced from thermal reactions was thought to be too long. In this paper, I
show that the previous conclusions are not always true depending on the
reaction for bosonic DM because of the Bose-enhanced reaction at very low
momentum. By using the simple $1\leftrightarrow 2$ decay/inverse decay process
to produce the DM, I demonstrate that the eV range bosonic DM can be thermally
produced $coldly$ from a hot plasma by performing a model-independent analysis
applicable to axion, hidden photon, and other bosonic DM candidates. Therefore,
the bosonic DM in the eV mass range may still be special and theoretically
well-motivated.
