Superconducting insertion devices, which produce periodic magnetic fields, have been built and installed in a number of synchrotron-light source storage-rings. For the most part, these devices have been wigglers, which have relatively long period lengths. This report concerns itself with the special cryogenic issues associated with short period undulators. The motivation for considering the incorporation of superconducting technology in insertion device designs is to achieve higher magnetic fields than can be achieved with more conventional permanent magnet technology. Since the peak field decreases sharply with increased magnet gap to period ratio, the cryogenic design of the magnet system is crucial. In particular, the insulation required for a warm vacuum bore device is impractical for short period undulators. This report describes the issues that are related to a cold bore (~4 K) and an intermediate temperature bore (30 to 70 K) designs. The criteria for the use of small cryocoolers for cooling a short period undulator are presented. The problems associated with connecting small coolers to an undulator at 4.2 K are discussed.