  We predict that a temperature gradient can induce a magnon-mediated spin Hall
response in an antiferromagnet with non-trivial magnon Berry curvature. We
develop a linear response theory which gives a general condition for a Hall
current to be well defined, even when the thermal Hall response is forbidden by
symmetry. We apply our theory to a honeycomb lattice antiferromagnet and
discuss a role of magnon edge states in a finite geometry.
