  In a previous paper, we presented the global solution of a new accretion flow
model, namely luminous hot accretion flows (LHAFs). In this {\em Letter}, we
first show the corresponding thermal equilibrium curve of LHAFs in the mass
accretion rate vs. surface density diagram. Then we examine its thermal
stability again local perturbations. We find that LHAFs are thermally unstable
when thermal conduction is neglected. However, when the accretion rate is not
very large, the timescale of the growth of perturbations is longer than the
accretion timescale, therefore the instability has no dynamical effect on the
accretion flow. When the accretion rate is large, the perturbations can grow
very fast at a certain radius. As a result, some cold clumps may form and the
accretion flow will become multi-phase.
