  The effects of radial advection and thermal diffusion were considered in
investigating the linear stability of an optically thin, two-temperature
accretion disc. If the disc has only very little advection, we proved that the
thermal instability exists when the disc is geometrically thin. But it dispears
in a geometrically slim disc if the thermal diffusion was considered. Moreover,
if the disc is advection dominated, the thermal instability does not exist. In
addition, we found that the instabilities of inertial-acoustic modes exist only
in a geometrically thin disc or an advection-dominated disc with low Mach
number, whereas the Lightman & Eardley viscous instability always dispears in a
two-temperature disc. A simple comparison also showed that an optically thin,
bremsstrahlung cooling dominated disc is generally more thermally unstable than
a two-temperature disc if it is not advection-dominated.
