Several polymers like ethylene glycol exhibit non-Newtonian rheological behavior. Ethylene glycol is a world-widely used engine coolant and therefore, investigation of thermal enhancement by dispersing mono and hybrid nanoparticles in ethylene glycol is worthful. Since ethylene glycol has shear rate-dependent viscosity and it obeys the power-law rheological model. Therefore, based on these facts, the power-law rheological model with thermophysical properties is augmented with basic law of heat transfer in fluid for the modeling of the considered physical situation. Mo{S}_{2} are taken as mono-nanoparticles where Mo{S}_{2} and Si{O}_{2} are taken as hybrid nanoparticles. Comparative study for the enhancement of thermal performance of MoS2 ethylene glycol and Mo{S}_{2}−Si{O}_{2}– ethylene glycol is done. For energy conservation, non-Fourier’s law of Cattaneo–Christov is used. The power-law fluid becomes more heat generative due to the dispersion of Mo{S}_{2} and Si{O}_{2}. However, Mo{S}_{2}−power-law fluid is less heat generative relative to Mo{S}_{2}− Si{O}_{2}-nanofluid. Thermal relaxation time is found proportional to the ability of the fluid to restore its thermal equilibrium.