Dark matter may be coupled to dark radiation: light degrees of freedom that mediate forces between dark sector particles. Cosmological constraints favor dark radiation that is colder than Standard Model radiation. In models with fixed couplings between dark matter and the Standard Model, these constraints can be difficult to satisfy if thermal equilibrium is assumed in the early universe. We construct a model of asymmetric reheating of the visible and dark sectors from late decays of a long-lived particle (for instance, a modulus). We show, as a proof of principle, that such a model can populate a sufficiently cold dark sector while also generating baryon and dark matter asymmetries through the out-of-equilibrium decay. We frame much of our discussion in terms of the scenario of dissipative dark matter, as in the Double-Disk Dark Matter scenario. However, our results may also be of interest for other scenarios like the Twin Higgs model that are in danger of overproducing dark radiation due to nonnegligible dark-visible couplings.