A lubricant composition having an enhanced thermal conductivity, up to 80% greater than its conventional analogues, and methods of preparation for these fluids are identified. One preferred composition contains a base oil, nanomaterial, and a dispersing agent or surfactant for the purpose of stabilizing the nanomaterial. One preferred nanomaterial is a high thermal conductivity graphite, exceeding 80 W/m in thermal conductivity. The graphite is ground, milled, or naturally prepared to obtain a mean particle size less than 500 nm in diameter, and preferably less than 100 nm, and most preferably less than 50 nm. The graphite is dispersed in the fluid by one or more of various methods, including ultrasonication, milling, and chemical dispersion. Carbon nanostructures such as nanotubes, nanofibrils, and nanoparticles are another type of graphitic structure useful in the present invention. Other high thermal conductivity carbon materials are also acceptable. To confer long-term stability, the use of one or more chemical dispersants or surfactants is useful. The thermal conductivity enhancement, compared to the fluid without graphite, is proportional to the amount of nanomaterials added. The graphite nanomaterials contribute to the overall fluid viscosity, partly or completely eliminating the need for viscosity index improvers and providing a very high viscosity index. Particle size and dispersing chemistry is controlled to get the desired combination of viscosity and thermal conductivity increase from the base oil while controlling the amount of temporary viscosity loss in shear fields. The resulting fluids have unique properties due to the high thermal conductivity and high viscosity index of the suspended particles, as well as their small size.