Stimulated Rayleigh-Mie scattering (SRMS) in two-photon absorption liquids is realized by a Fourier-transform-limited pulsed Nd-glass laser. For the first time, to the best of our knowledge, we have measured anti-Stokes spectral shifts of SRMS in toluene and hexane colloids of Ag nanoparticles, as well as in pure toluene. These values appreciably exceed the Rayleigh line width in those liquids. The four-wave mixing method is applied both experimentally and theoretically to display the process as Rayleigh-induced parametric generation. We show that the amplification effect is provided predominantly by thermally induced coherent polarization oscillations, while an interference-assisted thermal grating provides formation of a self-induced optical cavity inside the interaction region.