Shorter period undulators typically require a higher on-axis magnetic field in order to achieve a practical deflection parameter, K. Recent simulations and experiments have demonstrated that high-temperature superconducting (HTS) undulators, constructed from staggered-array bulk superconductors, can generate high undulator fields with period length as short as 10 mm. This advanced HTS technology has the potential to significantly enhance the photon energy range of synchrotron radiation light sources and free electron laser facilities. This paper reports on the progress made in developing of a 50-period bulk HTS undulator with period length of 12 mm for Shanghai soft x-ray free electron laser facility. It details the engineering design of the undulator prototype, thermal and mechanical analysis of the HTS variable temperature insert, and the current status of the system.