Many experiments with pulsed ion beams benefit from or even require ion bunches with both small temporal width as well as small energy spread. To achieve optimal ion-beam preparation, a buffer-gas filled cryogenic Paul trap is being developed in the context of the Multi Ion Reflection Apparatus for Collinear Laser Spectroscopy (MIRACLS). There, ion bunches of short-lived radionuclides are trapped in a Multi-Reflection Time-of-Flight (MR-ToF) device. Thus, the ions can be repeatedly probed by a laser beam compared to only once in conventional, single-passage collinear laser spectroscopy. To fulfill MIRACLS’ opposing requirements of a small temporal ion-bunch width and small energy spread, a buffer-gas filled cryogenic Paul trap is envisioned. Ion-optical simulations confirm the advantages of cryogenic temperatures and the linear scaling of the beam emittance as a function of the buffer-gas temperature. Beyond MIRACLS, high-quality ion beams from a cryogenic Paul trap will be beneficial for other precision experiments at radioactive ion beam facilities.