An electrospray ion source has been coupled to a cryogenic electrostatic ion-beam storage ring to enable experimental studies of the fundamental properties of biomolecular ions and their reactions in the gas phase on longer timescales than with previous instruments. Using this equipment, we have measured the vibrational radiative cooling rate of the deprotonated anion of the chromophore of the cyan fluorescent protein, a color-shifted mutant of the iconic green fluorescent protein. Time-resolved dissociation rates of collisionally activated ions are first measured to benchmark a model of the dissociation rate coefficient. Storage time-dependent laser-induced dissociation rates are then measured to probe the evolution of the internal energy distribution of the stored ion ensemble. We find that significant heating of the electrosprayed ions occurs upon their extraction from the ion source, and that the radiative cooling rate is consistent with the prediction of a simple harmonic cascade model of vibrational relaxation.