Uranyl nitrate hexahydrate [UO2(NO3)2 · 6H2O] (UNH) holds interest as a potential nuclear reactor fuel for manufacturing the key medical isotope 99mTc through the production and subsequent decay of 99Mo. Fuel element design for such a production method requires knowledge of the thermal properties of the fuel material, particularly in the case of UNH, which has a significantly lower melting temperature than that of fuels being used currently. A system was designed to measure the thermal conductivity of UNH by an ASTM International standard thermal probe method. Measurements were made at four temperatures within the relevant range for the reactor system (25°C through 55°C) and with a variety of material preparations. With a fill gas of air, the results demonstrate a thermal conductivity at 25°C between 0.07 and 0.10 W · cm−1 · K−1. The results are the first step toward future studies that could lead to a more efficient reactor design with a heating source term capable of meeting the demand for 99Mo production while maintaining a safe and effective thermal margin.