  Self-gravitating stellar disks with random motion support both exponentially
growing and, in some cases, purely oscillatory axisymmetric bending modes,
unlike their cold disk counterparts. A razor-thin disk with even a very small
degree of random motion in the plane is both unstable and possesses a discrete
spectrum of neutral modes, irrespective of the sharpness of the edge. Random
motion normal to the disk plane has a stabilizing effect but at the same time
allows bending waves to couple to the internal vibrations of the particles,
which causes the formerly neutral modes to decay through Landau damping.
  Focusing first on instabilities, I here determine the degree of random motion
normal to the plane needed to suppress global, axisymmetric, bending
instabilities in a family of self-gravitating disks. As found previously,
bending instabilities are suppressed only when the thickness exceeds that
expected from a na\"\i ve local criterion when the degree of pressure support
within the disk plane is comparable to, or exceeds, the support from rotation.
A modest disk thickness is adequate for the bending stability of most disk
galaxies, except perhaps near their centers.
  The discretization of the neutral spectrum in a zero-thickness disk is due to
the existence of a turning point for bending waves in a warm disk, which is
absent when the disk is cold. When the disk is given a finite thickness, the
discrete neutral modes generally become strongly damped through wave-particle
interactions. It is surprising therefore that I find some simulations of warm,
stable disks can support (quasi-)neutral, large-scale, bending modes that decay
very slowly, if at all.
