The linear stability analysis has been performed for the thermocapillary liquid layers of a shear-thinning fluid. The Carreau fluid model is applied to describe the rheological property. The critical parameters are determined as a function of Prandtl number (Pr), degree of shear-thinning, and gravity level. For linear flow, the shear-thinning effect is destabilizing for small and moderate Pr but increases the stability slightly for large Pr. For return flow, the perturbation kinetic energy concentrates near the surface, and the flow is stabilized when the surface viscosity is used. The streamwise wave is excited at large Pr, and a new mechanism is found at moderate Pr, where the hot spots appear at the bottom of the layer. In the presence of gravity, the viscosity stratification is enhanced and more kinds of different modes are excited. The preferred mode changes to downstream at large Pr while the gravity becomes an important perturbation energy source at small Pr. The shear-thinning effect for the instability mechanism is discussed and the comparisons are made with channel flows. Published by AIP Publishing.