  We present a systematic study of the nonlinear thermal Hall responses in
bosonic systems using the quantum kinetic theory framework. We demonstrate the
existence of an intrinsic nonlinear boson thermal current, arising from the
quantum metric which is a wavefunction dependent band geometric quantity. In
contrast to the nonlinear Drude and nonlinear anomalous Hall contributions, the
intrinsic nonlinear thermal conductivity is independent of the scattering
timescale. We demonstrate the dominance of this intrinsic thermal Hall response
in topological magnons in a two-dimensional ferromagnetic honeycomb lattice
without Dzyaloshinskii-Moriya interaction. Our findings highlight the
significance of band geometry induced nonlinear thermal transport and motivate
experimental probe of the intrinsic nonlinear thermal Hall response with
implications for quantum magnonics.
