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The Alpha Magnetic Spectrometer (AMS) is a particle physics experiment for use on the International Space Station (ISS). At the heart of the detector will be a large superconducting magnet cooled to a temperature of 1.8 K by superfluid helium. The helium is contained in a toroidal vessel with a volume of approximately 2500 liters. From ground safety and flight safety considerations, the system must be safe in the event of a sudden catastrophic loss of insulating vacuum. A test facility has been designed and built by the magnet designer and fabricator, Space Cryomagnetics Ltd. of Culham, England. This facility allows a sudden, total loss of vacuum event in a small (12 liter) superfluid helium vessel to be triggered and monitored, so that venting rates and heat fluxes can be calculated. This paper describes the design of the test facility and the results of experiments to determine the heat flux to the superfluid helium. Test results are given for a completely uninsulated vessel, and for a vessel insulated with a thin coating of a special, lightweight insulating material.