  Predictivity of many non-thermal dark matter (DM) models is marred by the
gravitational production background. This problem is ameliorated in models with
lower reheating temperature $T_R$, which allows for dilution of gravitationally
produced relics. We study the freeze-in dark matter production mechanism in the
thermal bath with the electroweak scale temperature. The process is
Boltzmann-suppressed if the dark matter mass is above $T_R$. In this case, the
coupling to the thermal bath has to be significant to account for the observed
dark matter relic density. As a result, the direct DM detection experiments
already probe such freeze-in models, excluding significant parts of parameter
space. The forthcoming experiments will explore this framework further,
extending to lower couplings and higher reheating temperatures.
