We present a class of dark matter models, in which the dark matter particle is a feebly interacting massive particle (FIMP) produced via the decay of an electrically charged and/or colored parent particle. Given the feeble interaction, dark matter is produced via the freeze-in mechanism and the parent particle is long-lived. The latter leads to interesting collider signatures. We study current LHC constrains on our models arising from searches for heavy charged particles, disappearing tracks, displaced leptons and displaced vertices. We demonstrate not only that collider searches can be a powerful probe of the freeze-in dark matter models under consideration, but that an observation can lead as well to interesting insights on the reheating temperature and thus on the validity of certain baryogenesis models.