  We study the chiral properties of domain-wall quarks at high temperatures on
an ensemble of quenched configurations. Low lying eigenmodes of the Dirac
operator are calculated and used to check the extent to which the Atiyah-Singer
index theorem is obeyed on lattices with finite $N_5$. We calculate the
connected and disconnected screening propagators for the lowest mass scalar and
pseudoscalar mesons in the sectors of different topological charge and note
that they behave as expected. Separating out the would-be zero eigenmodes
enables us to accurately estimate the disconnected propagators with far less
effort than would be needed otherwise.
