  In many cases accretion proceeds from disks onto planets, stars, white
dwarfs, and neutron stars via a boundary layer, a region of intense shear where
gas transitions from a near-Keplerian speed to that of the surface. These
regions are \textit{not} susceptible to the common magnetorotational and
Kelvin-Helmholtz instabilities, and instead global modes generated by
supersonic shear instabilities are a leading candidate to govern transport in
these regions. This work investigates the dynamics of these systems under a
range of thermodynamic conditions, surveying both disk sound speeds and cooling
rates. Very fast or very slow cooling has little effect on wave dynamics: in
the fast-cooling limit, waves propagate in an effectively isothermal manner,
and in the slow limit wave propagation is effectively adiabatic. However, when
the cooling timescale is comparable to the wave period, wave damping becomes
extreme. In cases with intermediate cooling rates, mass and angular momentum
transport can be suppressed by orders of magnitude compared to isothermal and
uncooled cases. Cooling in accretion disks leads to a preference for
wavenumbers near and below the Mach number of the disk; the corresponding lower
frequencies can (in non-isothermal systems) couple to gravity modes within the
star, potentially causing low-frequency variability such as dwarf nova and
quasi-periodic oscillations in accreting systems.
