This work presents a device of novel design capable of measuring the thermal conductivity of polymeric materials, either armed with nanoparticles (nanocomposites) or not. The new design uses two hemispheric tanks containing cold and hot liquid, respectively, each of them wetting one side of a disc-shaped polymeric sample. Proper selection of construction materials (aluminum body, Teflon fittings etc) and geometry (shape, size, etc) of the Cold/Hot tanks and the sample (diameter, thickness) made possible to acquire reliable values of the low thermal conductivity of several polymeric samples. This is so despite the uneven surface of the exposed samples to the wetting liquids and the poor homogeneity observed in the nanocomposite material. The above are unique features of the new device. Experiments are performed placing the disc-shaped sample (15 cm diameter, 1, 3, 4.31 & 6.07 mm thickness) in between the two hemisphere tanks of the device, both filled with water: one at 45°C and the other at 25°C. (Figure 1). The thermal conductivity of several materials was measured such as silicone rubber and epoxy polymers with a variety of mixtures of cross-links, Epon828 30:70 (D230:D2000), Epon828 40:60 (D230:D2000) and Epon828 50:50 (D230:D2000). Silicone rubber and Epon828 50:50 (D230:D2000) tested as nanocomposite materials with 3% by volume MCF and I30 E nanoparticles. The following results were observed: i) Low thermal conductivity across all aforementioned materials, ii) different mixtures of cross-links did not affect the thermal conductivity of polymers, iii) the introduction of nanomaterials increases the thermal conductivity of resulting nanocomposite materials. The next goal is to miniaturize the device in order to measure the thermal conductivity of much smaller diameter samples (~ 2cm) (Figure 2).