The resonant optical excitation of dielectric nanostructures offers unique opportunities for developing remarkable nanophotonic devices. Light that is structured by tailoring the vectorial characteristics of the light beam provides an additional degree of freedom in achieving flexible control of multipolar resonances at the nanoscale. Here, we investigate the nonlinear scattering of subwavelength silicon (Si) nanostructures with radially and azimuthally polarized cylindrical vector beams to show a strong dependence of the photothermal nonlinearity on the polarization state of the applied light. The resonant magnetic dipole, selectively excited by an azimuthally polarized beam, enables enhanced photothermal nonlinearity, thereby inducing large scattering saturation. In contrast, radially polarized beam illumination shows no observable nonlinearity owing to off-resonance excitation. Numerical analysis reveals a difference of more than 2 orders of magnitude in photothermal nonlinearity under two types of polarization excitations. Nonlinear scattering and the unique doughnut-shaped focal spot generated by the azimuthally polarized beam are demonstrated as enabling far-field high-resolution localization of nanostructured Si with an accuracy approaching 50 nm. Our study extends the horizons of active Si photonics and holds great potential for label-free superresolution imaging of Si nanostructures.