  The absence of any confirmative signals from extensive DM searching motivates
us to go beyond the conventional WIMPs scenario. The feebly interacting massive
particles (FIMPs) paradigm provides a good alternative which, despite of its
feebly interaction with the thermal particles, still could correctly produce
relic abundance without conventional DM signals. The Infrared-FIMP based on the
renormalizable operators is usually suffering the very tiny coupling drawback,
which can be overcome in the UltraViolet-FIMP scenario based on high
dimensional effective operators. However, it is sensitive to the history of the
very early Universe. The previous works terminates this sensitivity at the
reheating temperature $T_{RH}$. We, motivated by its UV-sensitivity,
investigate the effects from the even earlier Universe, reheating era. We find
that in the usual case with $T_{RH}\gg m_{\rm DM}$, the production rate during
reheating is very small as long as the effective operators dimension $d \leq
8$. Besides, we consider the contribution from the mediator, which may be
produced during reheating. Moreover, we study the situation when $T_{RH}$ is
even lower than $m_{\rm DM}$ and DM can be directly produced during reheating
if its mass does not exceed $T_{MAX}$.
