The multi-photon photodissociation action spectrum of the coronene cation (C24H12+) has been measured in the cryogenic electrostatic storage ring DESIREE (Double ElectroStatic Ion Ring ExpEriment) as a function of storage time. These measurements reveal not only the intrinsic absorption profile of isolated coronene cations, but also the rate at which hot-band absorptions are quenched by radiative cooling. Just after injection, the action spectrum is severely reddened by hot-band absorptions. These hot bands fade with a time constant of 200 ms, which is consistent with radiative cooling via infrared emission from vibrational transitions. A comparison of the present results to those obtained in cryogenic ion trap experiments is discussed at length.