Scintillating calorimeters are cryogenic detectors combining a measurement of scintillation with one of phonons to provide particle identification. In view of developing alkali halide devices of this type able to check the DAMA/LIBRA claim for the observation of dark matter, we have simulated detector performances to determine their sensitivity by two methods with little model-dependence. We conclude that if performance of the phonon channel can be brought in line with those of other materials, an exposure of 10 kg-days would suffice to check the DAMA/LIBRA claim in standard astrophysical scenarios. Additionally, a fairly modest array of 5 kg with background rejection would be able to directly check the DAMA/LIBRA modulation result in 2 years. Comment: 22 pages, 6 figures
