The effects of radial advection and thermal diffusion were considered
in investigating the linear stability of an optically thin, two-temper
ature accretion disc. If the disc has very little advection, we prove
that the thermal instability exists when the disc is geometrically thi
n. However, it disappears in a geometrically slim disc if the thermal
diffusion is considered. Moreover, if the disc is advection-dominated,
the thermal instability does not exist. We also found that the instab
ilities of inertial-acoustic modes exist only in a geometrically thin
disc or an advection-dominated disc with a low Mach number, whereas th
e Lightman & Eardley viscous instability always disappears in a two-te
mperature disc. A simple comparison also showed that an optically thin
, bremsstrahlung cooling-dominated disc is generally more thermally un
stable than a two-temperature disc if it is not advection-dominated.