Shear-thinning behavior (decrease of the apparent steady viscosity with shear) due to breaking of weak particle flocs and posterior alignment of individual particles in layers parallel to the flow direction is usually observed before the appearance of the shear-thickening behavior (increase of the apparent steady viscosity with shear). The shear-thickening behavior is mainly due to the dominant role played by hydrodynamic over Brownian and colloidal forces at relatively high shear. As a rule, the onset of shear-thickening behavior and the maximum viscosity value appear at lower shear rates when solid concentration increases, and temperature decreases. However, the influence of solid concentration and temperature on shear stress characteristic values have received less attention despite being the shear stress the true cause of microstructure changes that can provoke the appearance of the shear-thickening behaviour. A recently published empirical equation for the shear stress dependence of the steady viscosity of shear thickening fluids [T. Shende, V.J. Niasar, M. Babaei, J. Mol. Liq. 325 (2021) 115220] has been used for fitting experimental data (MARSIII, Thermo-Haake, Germany) of a hydrophilic fumed silica suspension (A200 (Evonik, Germany) in PPG400 (Sigma-Aldrich, Germany)). The influence of temperature (10,\ 30,\ 50,\ 70\degc) and solid concentration (10,\ 15,\ 20,\ 25%\ wt) on the shear-thickening behavior has been monitored recording their influence on the model parameters.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech