A stable and homogeneous grease based on carbon nanotubes (CNTs, single-wall and multi-wall) in polyalphaolefin oil has been produced without using a chemical surfactant. For example, for a 11 wt% (7 vol%) single-wall CNT (diameter 1–2 nm, length 0.5–40 μm) loading, the thermal conductivity (TC) of the grease shows a 60–70% increase compared to that for no nanotube loading. In addition, the grease is electrically conductive, has a high dropping point, good temperature resistance, and does not react with copper at temperatures up to 177 °C. The performance of carbon nanotube grease could be much better with the improvement of nanotube quality and purity. A possible explanation for these results is that of a high loading of CNTs (>10 wt%), they become associated with each other by van der Waals forces in the grease to form three-dimensional percolation networks. Time-dependent magnetic results demonstrate that, even under the influence of a strong outside magnetic field, the TC value remains constant. This phenomenon can be attributed to the existence of networks that makes magnetic alignment of nanotubes impossible.