  Thermal instability is examined for advection-dominated one-temperature
accretion disks. We consider axisymmetric perturbations with short wavelength
in the radial direction. The viscosity is assumed to be sufficiently small for
the vertical hydrostatic balance to hold in perturbed states. The type of
viscosity is given either by the $\alpha$-viscosity or by a diffusion-type
stress tensor. Optically thick disks are found to be in general more unstable
than optically thin ones. When the thermal diffusion is present, the optically
thin disks become stable, but the optically thick disks are still unstable. The
instability of the advection-dominated disks is different from that of the
geometrically thin disks without advection. In the case of no advection, the
thermal mode behaves under no appreciable surface density change. In the case
of advection-dominated disks, however, the thermal mode occurs with no
appreciable pressure change (compared with the density change), when local
perturbations are considered. The variations of angular momentum and of surface
density associated with the perturbations lead to a thermal instability. The
astrophysical implications of this instability are briefly discussed.
