  We present a study of the thermal Hall effect in the extended Heisenberg
model with $XXZ$ anisotropy in the kagome lattice. This model has the
particularity that, in the classical case, and for a broad region in parameter
space, an external magnetic field induces a chiral symmetry breaking: the
ground state is a doubly degenerate $q=0$ order with either positive or
negative net chirality. Here, we focus on the effect of this chiral phase
transition in the thermal Hall conductivity using Linear-Spin-Waves theory. We
explore the topology and calculate the Chern numbers of the magnonic bands,
obtaining a variety of topological phase transitions. We also compute the
magnonic effect to the critical temperature associated with the chiral phase
transition ($T_c^{SW}$). Our main result is that, the thermal Hall
conductivity, which is null for $T>T_c^{SW}$, becomes non-zero as a consequence
of the spontaneous chiral symmetry breaking at low temperatures. Therefore, we
present a simple model where it is possible to "switch" on/off the thermal
transport properties introducing a magnetic field and heating or cooling the
system.
