We consider a class of models where the Standard Model (SM) and dark matter (DM) belong to a conformal/scale-invariant theory at high energies. The scale invariance is broken spontaneously at scale f , and the corresponding Goldstone boson is the dilaton. In the low-energy theory, we assume DM interacts with the SM only through the dilaton portal suppressed by the conformal breaking scale f . Assuming f TeV, the portal interactions are very feeble, and hence the DM is not in thermal equilibrium with the SM bath. Therefore, ultraviolet freeze-in production of DM is realized through the dilaton portal, which is most effective at the maximum temperature of the SM bath. The temperature evolution critically depends on the reheating dynamics, which we parameterize by a general equation of state w and temperature at the end of reheating T rh . Implications of the reheating dynamics are studied for DM production in this framework. We have identified regions of parameter space that lead to the observed DM relic abundance for a wide range of DM masses and reheating temperatures for a scalar, vector, or fermion DM.