  Recently, Medvedev & Narayan (2001) discovered a new type of accretion flow,
a hot settling flow around a rapidly rotating neutron star. The flow is
cooling-dominated and energetically similar to the Shapiro, Lightman, & Eardley
(1976, SLE) solution. Since the SLE solution is known to be thermally unstable,
one might suspect that the new solution would also be unstable. However, due to
the very high temperature of the accreting gas, thermal conduction is very
strong and could suppress the thermal instability. We analyze the role of
thermal conduction in both the hot settling flow and the SLE solution. In the
hot settling flow collisions are very rare. Therefore, thermal transport occurs
via free streaming of electrons along tangled magnetic field lines. We find
that conduction is strong enough to make the flow marginally stable. In
contrast, in the cooler SLE solution, conduction is via collisional,
Spitzer-type transport. In this case, conduction is weaker, and we find that
the SLE solution is thermally unstable even in the presence of conduction.
