  This letter expands the stability criterion for radially stratified,
vertically {unstratified} accretion disks incorporating thermal relaxation. We
find a linear amplification of epicyclic oscillations in these disks that
depends on the effective cooling time, i.e. an overstability. The growth rates
of the overstability vanish for both extreme cases, e.g. infinite cooling time
and instantaneous cooling, i.e. the adiabatic and fully isothermal cases.
However, for thermal relaxation times $\tau$ on the order of the orbital
frequency, $\tau\Omega \sim 1$, modes grow at a rate proportional to the square
of the Brunt-V\"ais\"al\"a frequency. The overstability is based on epicyclic
motions, with the thermal relaxation causing gas to heat while radially
displaced inwards, and cool while radially displaced outwards. This causes the
gas to have a lower density when moving outwards compared to when it moves
inwards, so it feels the outwards directed pressure force more strongly on that
leg of the journey. We suggest the term ``Convective Overstability" for the
phenomenon that has already been numerically studied in the non-linear regime
in the context of amplifying vortices in disks, under the name ``Subcritical
Baroclinic Instability". The point of the present paper is to make clear that
vortex formation in three-dimensional disks is neither subcritical, i.e. does
not need a finite perturbation, nor is it baroclinic in the sense of
geophysical fluid dynamics, which requires on vertical shear. We find that
Convective Overstability is a linear instability that will operate under a wide
range of physical conditions for circumstellar disks.
