We have studied the photodissociation of CH^{+} in the Cryogenic Storage Ring at ambient temperatures below 10 K. Owing to the extremely high vacuum of the cryogenic environment, we were able to store CH^{+} beams with a kinetic energy of ∼60 keV for several minutes. Using a pulsed laser, we observed Feshbach-type near-threshold photodissociation resonances for the rotational levels J=0-2 of CH^{+}, exclusively. In comparison to updated, state-of-the-art calculations, we find excellent agreement in the relative intensities of the resonances for a given J, and we can extract time-dependent level populations. Thus, we can monitor the spontaneous relaxation of CH^{+} to its lowest rotational states and demonstrate the preparation of an internally cold beam of molecular ions.