Nanofluids have received much attention due, in part, to the range of properties possible with different combinations of nanoparticles and base fluids. In this work, we measure the viscosity of suspensions of graphite particles in ethylene glycol as a function of the volume fraction, shear rate, and temperature below and above the percolation threshold. We also measure and contrast the trends observed in the viscosity with increasing volume fraction to the thermal conductivity behavior of the same suspensions: above the percolation threshold, the slope that describes the rate of thermal conductivity enhancement with concentration reduces compared to below the percolation threshold, whereas that of the viscosity enhancement increases. While the thermal conductivity enhancement is independent of temperature, the viscosity changes show a strong dependence on temperature and exhibit different trends with respect to the temperature at different shear rates above the percolation threshold. Interpretation of the experimental observations is provided within the framework of Stokesian dynamics simulations of the suspension microstructure, and suggest that although diffusive contributions are not important for the observed thermal conductivity enhancement, they are important for understanding the variations in the viscosity with changes of temperature and shear rate above the percolation threshold. The experimental results can be collapsed to a single master curve through calculation of a single dimensionless parameter (a Peclet number based on the rotary diffusivity of the graphite particles).