  Hydrodynamical interactions between binaries and circumbinary disks (CBDs)
play an important role in a variety of astrophysical systems, from young
stellar binaries to supermassive black hole binaries. Previous simulations of
CBDs have mostly employed locally isothermal equation of state. We carry out
two-dimensional viscous hydrodynamic simulations of CBDs around equal-mass,
circular binaries, treating the gas thermodynamics by thermal relaxation
towards equilibrium temperature (the constant-$\beta$ cooling ansatz, where
$\beta$ is the cooling time in units of the local Keplerian time). As an
initial study, we use the grid-based code Athena++ on a polar grid, covering an
extended disk outside the binary co-orbital region. We find that with a longer
cooling time, the accretion variability is gradually suppressed, and the
morphology of the CBD becomes more symmetric. The disk also shows evidence of
hysterisis behavior depending on the initial conditions. Gas cooling also
affects the rate of angular momentum transfer between the binary and the CBD,
where given our adopted disk thickness and viscosity ($H/r\sim 0.1$ and
$\alpha\sim 0.1$), the binary orbit expands while undergoing accretion for most
$\beta$ values between 0 and 4.0 except over a narrow range of intermediate
$\beta$ values. The validity of using polar grid excising the central domain is
also discussed.
