At the temperature 293 K, the influence of two types of nanoimpurities (carbon multiwall nanotubes and C60 fullerene) both separately and together on the dielectric properties of Shell oil transformer oil has been studied. It has been shown that these impurities do not significantly effect on the value of the dielectric permittivity of Shell oil, but more significantly increase its conductivity. It has been found that in the presence of nanotubes inside Shell oil, the dependence of its electrical conductivity on the fullerene concentration is nonmonotonic. The samples with the fullerene concentration 100 ppm have the highest conductivity. At the fullerene concentration 300 ppm, the conductivity of Shell oil with the impurities of carbon nanotube and C60 fullerene becomes almost equal to the electrical conductivity of Shell oil only with the impurities of carbon nanotubes. It has been suggested that C60 fullerene can be used to reduce the electrical conductivity of Shell oil with magnetic nanoparticles required to increase the cooling efficiency of transformers under the action of their own magnetic field.