This paper addresses the question whether ion storage rings advantageously could be used for studies of dissociative recombination of molecular ions. We have used a particular ion, HeH+, and a particular storage ring, CRYRING, in a case study. Vibrational relaxation times in ground state HeH+ have been calculated by means of an electric dipole moment function obtained from multi-reference CI wave functions. Parameters for CRYRING, including its electron cooler section, have been used to estimate storage times for HeH+, and expected count rates in a dissociative recombination experiment. It is shown that the expected storage time of HeH+ is two,orders of magnitude larger than the vibrational lifetimes, hence experiments with vibrationally cooled ions can be anticipated. The expected count rate is such that three orders of magnitude less ions than normally used in CRYRING (10(9)) is sufficient.