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Fermilab is in the process of constructing a 60 MeV linac as part of the High Intensity Neutrino Source (HINS) R&D program. Developments from this program could play a direct role in an upgraded injector for the existing Main Injector at Fermilab to support the ongoing neutrino physics program. In addition this same R&D could lead to breakthroughs in superconducting radio frequency (SRF) technology useful in any of several large-scale SRF accelerator projects being discussed around the world. The initial beam acceleration in the linac front end is achieved using room temperature spoke resonators combined with superconducting solenoids for focusing. At the end of the room temperature section, three cryomodules containing either 9 or 11 single spoke resonators operating at 4.5 K and 325 MHz, also with superconducting solenoids, accelerate the H-test beam to its final energy. Each spoke cavity will be tested individually in a cryostat that replicates conditions in the longer multi-cavity modules. This test cryostat has all the features of the longer cryomodules-magnetic shielding, 80 K thermal shield, multi-layer insulation, support post, and input coupler. The goal is that by using common features we will facilitate the eventual design of the longer cryomodules. This paper describes the design of the test cryostat, the mechanical design of the spoke cavities and their helium vessels, and includes a detailed status of the development work.