  We present a series of simulations in both pure hydrodynamics (HD) and
magnetohydrodynamics (MHD) exploring the degree to which alignment of disks
subjected to external precessional torques (e.g., as in the `Bardeen-Petterson'
effect) is dependent upon the disk sound speed c_s. Across the range of sound
speeds examined, we find that the influence of the sound speed can be
encapsulated in a simple "lumped-parameter" model proposed by Sorathia et al.
(2013a). In this model, alignment fronts propagate outward at a speed ~0.2
rOmega_precess(r), where Omega_precess is the local test-particle precession
frequency. Meanwhile, transonic radial motions transport angular momentum both
inward and outward at a rate that may be described roughly in terms of an
orientation diffusion model with diffusion coefficient ~2c_s^2/Omega, for local
orbital frequency Omega. The competition between the two leads, in isothermal
disks, to a stationary position for the alignment front at a radius
proportional to c_s^(-4/5). For alignment to happen at all, the disk must
either be turbulent due to the magnetorotational instability in MHD, or, in HD,
it must be cool enough for the bending waves driven by disk warp to be
nonlinear at their launch point. Contrary to long-standing predictions, warp
propagation in MHD disks is diffusive independent of the parameter c_s/(alpha
v_orb$, for orbital speed v_orb and ratio of stress to pressure of alpha. In
purely HD disks, i.e., those with no internal stresses other than bulk
viscosity, warmer disks align weakly or not at all; cooler disks align
qualitatively similarly to MHD disks.
