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The superconducting undulator (SCU) is a trend to be applied for future light sources to obtain the higher light brilliance. A planar SCU prototype with a period of 16 mm, a magnetic gap of 9.5 mm and 50-periods magnet has been under development at the Shanghai Synchrotron Radiation Facility (SSRF) since late 2013. The key technologies including magnet cooling, coil winding, low-temperature alignment of magnet and beam tube, and cryogenic magnetic field measurement have been investigated. A cryocooler-cooled test cryostat was developed for the purpose of both experimentally studying the key technologies and testing the performance of the SCU prototype. Two-stage cryocoolers were applied for cool down, helium liquefaction and keeping the SCU cooled at operation. The SCU magnet and the UHV beam tube were cooled separately. The magnet working at 4.2 K is cooled by thermosiphon-driven liquid helium flowing through the piping in the magnet mandrel. The beam tube, thermal shields and binary leads were conduction-cooled. The beam tube will work at between 4.2 K and 20 K up to dynamic loads generated by the SSRF beam. A set of improved self-centered support assembly for the magnet was developed in order to avoid the complex alignment at low temperature and lower down the machining cost. A cooling approach to effectively cool the junction of the binary lead made of copper and HTS lead commonly used in cryocooler-cooled superconducting systems was adopted and validated. The cryostat was successfully debugged and run at the early of 2016. This paper describes the design details of the cryostat including new approaches to cool the SCU and the binary leads, its fabrication and test results. [ABSTRACT FROM AUTHOR]