We have designed and developed a new experimental setup, based on the 3-omega method, to measure thermal conductivity, heat capacity and electrical resistivity of a variety of samples in a broad temperature range (2-550 K) and under magnetic fields up to 9 T. The validity of this method is tested by measuring various types of metallic (copper, platinum, and constantan) and insulating (SiO_2) materials, which have a wide range of thermal conductivity values (1-400 Wm-1K-1). We have successfully employed this technique for measuring the thermal conductivity of two actinide single crystals, uranium dioxide, and uranium nitride. This new experimental approach for studying nuclear materials will help to advance reactor fuel development and understanding. We have also shown that this experimental setup can be adapted to the Physical Property Measurement System (Quantum Design) environment and/or other cryocooler systems.