We study the chiral properties of domain-wall quarks at high temperatures o
n 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 th
e connected and disconnected screening propagators for the lowest mass scal
ar and pseudoscalar mesons in the sectors of different topological charge a
nd note that they behave as expected. Separating out the would-be zero eige
nmodes enables us to accurately estimate the disconnected propagators with
far less effort than would be needed otherwise.