Nowadays, the reduction of the environmental impact associated with the operation of the oil industry is a primary concern. A growing trend is to develop low-toxicity formulations based on biodegradable components. In this sense, vegetable oils structured with nanomaterials could be an alternative to mineral or synthetic oils for sustainable fluid formulations. Hydrophobic fumed silica nanoparticles have the capability to change the rheological behavior of oil in suspensions, providing a large variety of non-Newtonian behaviors over a wide range of temperatures, from shear-thinning to gel-like, depending on the concentration and the nanosilica’s hydrophobicity, that permits the design of fluids with selected characteristic and applications. This work explores the microstructure and the rheological behavior of hydrophobic fumed silica dispersed in a sunflower oil as a function of temperature and pressure. The results suggest that the suspensions of hydrophobic silica in sunflower oil reveals appropriate rheological and thermal properties over a wide range of temperatures and pressures to serve as components of sustainable drilling fluids.