  Motivated by recent transport measurements in high-$T_c$ cuprate
superconductors in a magnetic field, we study the thermal Hall conductivity in
materials with topological order, focusing on the contribution from neutral
spinons. Specifically, different Schwinger boson mean-field ans\"{a}tze for the
Heisenberg antiferromagnet on the square lattice are analyzed. We allow for
both Dzyaloshinskii-Moriya interactions, and additional terms associated with
scalar spin chiralities that break time-reversal and reflection symmetries, but
preserve their product. It is shown that these scalar spin chiralities, which
can either arise spontaneously or are induced by the orbital coupling of the
magnetic field, can lead to spinon bands with nontrivial Chern numbers and
significantly enhanced thermal Hall conductivity. Associated states with
zero-temperature magnetic order, which is thermally fluctuating at any $T>0$,
also show a similarly enhanced thermal Hall conductivity.
