A steady state, axial flow thermal conductivity test apparatus was designed and constructed to operate between room temperature and approximately 4 Kelvin, and to be compatible with existing electronic instrumentation and a continuous flow cryostat. The test design included a radiation shield that had its temperature profile matched to that of the sample to minimize radiation heat transfer losses. The cryostat was used to provide the controllable, low temperature test environment in which the test apparatus would operate. A special wiring bundle was constructed to ensure proper connection of the test device to the required electronic instrumentation, which was controlled from a computer by custom written software. Once assembled, the thermal conductivity of a high purity copper sample was measured over the temperature range from 45 to 300 Kelvin and compared to literature recommended values. The test was performed a second time to check repeatability of the measurements over a range of temperature. Next, the thermal conductivity of a high purity niobium sample was measured and compared to literature recommended values. This test was also performed twice. When completed, these tests had demonstrated the accuracy and repeatability of the measurement of thermal conductivity by the test apparatus over the range of temperatures specified and over a range of conductivities. Finally, the thermal conductivity of a sample of the bulk metallic glass Vitreloy 1 was measured over the same temperature range. As far as was known, this was the first time the thermal conductivity of this particular material had been tested below 400 Kelvin. / Graduation date: 2003