The phenomenon of shear thickening has been studied in sterically stabilized colloidal suspensions. Temperature has been used to vary the solvent quality of the suspending medium for the grafted polymer in the stabilizer layer. A decrease in temperature causes the polymer coat to shrink. This results in a lower viscosity in the shear thinning region but also in a lower critical shear rate and shear stress at the onset of shear thickening. The critical shear stress increases with increasing particle volume fraction, at least for the volume fractions studied here. In large amplitude oscillatory flow, strain hardening for both storage and loss moduli sets in at the same peak shear rate that causes shear thickening in steady state flow. Parallel superposition also has been used to probe the effect of the stabilizer layer. The frequency dependence of the superposition moduli changes drastically once shear thickening sets in. Surprisingly, this: produces a simple and constant shape for the moduli-frequency curves with relaxation times that become nearly independent of the shear rate.