Nanomaterials have an excellent potential for improving the rheological and tribological properties of lubricating oil. In this study, oleic acid was used to surface-modify nanoparticles to enhance the dispersion and stability of Nanofluid. The surface modification was conducted for inorganic nanoparticles (NPs) TiO₂ and CuO with oleic acid (OA) surfactant, where oleic acid could render the surface of TiO2-CuO hydrophobic. Fourier transform infrared spectroscopy (FTIR), and Scanning electron microscopy (SEM) were used to characterize the surface modification of NPs. The main objective of this study was to investigate the influence of adding modified TiO₂-CuO NPs with weight ratio 1:1 on thermal-physical properties such as kinematic viscosity, viscosity index (VI), pour point, and flash point of Iraqi base oil (40 stock) and nano-lubricating oil. The kinematic viscosity of base oil at 40 °C and 100°C increased with high concentrations of modified TiO₂-CuO NPs. The highest value of VI of base oil 40 stock at 0.8 wt. % of modified TiO₂-CuO NPs was 108.5. The results showed that the flashpoint value increased with the increased concentration of modified TiO₂-CuO NPs of base oil 40, where the highest value was 220 °C. The pour point of nano lubricating oil base with 0.8 wt. % of modified TiO₂-CuO NPs showed decreasing from -12 °C to -15 °C of base oil 40.