This study is devoted to the instantaneous acoustic heating of a shear-thinning fluid. Apparent viscosity of a shear-thinning fluid depends on the shear rate. That feature distinguishes it from a viscous Newtonian fluid. The special linear combination of conservation equations in the differential form makes it possible to derive dynamic equations governing both the sound and non-wave entropy mode induced in the field of sound. These equations are valid in a weakly nonlinear flow of a shear-thinning fluid over an unbounded volume. They both are instantaneous, and do not require a periodic sound. An example of a sound waveform with a piecewise constant shear rate is considered as a source of acoustic heating.