  Optical heating of resonant nanostructures is one of the key issues in modern
nanophotonics, being either harmful or desirable effect depending on the
applications. Despite a linear regime of light-to-heat conversion is
well-studied both for metal and semiconductor resonant systems generalized as
critical coupling condition, the clear strategy to optimize optical heating
upon high-intensity light irradiation is still missing. In this work, we
propose a simple analytical model for such problem taking into account material
properties changes caused by the heating. It allows us to derive a new general
critical coupling condition for the nonlinear case, requiring counterintuitive
initial spectral mismatch between the pumping light frequency and resonant one.
Basing on the suggested strategy, we develop an optimized design for efficient
nonlinear optical heating, which employs a cylindrical nanoparticle supporting
quasi bound state in the continuum mode (quasi-BIC or so-called `super-cavity
mode') excited by the incident azimuthal vector beam. Our approach provides a
background for various nonlinear experiments related to optical heating and
bistability, where self-action of the intense laser beam can change resonant
properties of the irradiated nanostructure.
