  We investigate the thermal instability of a smooth equilibrium state, in
which the density function satisfies Schwarzschild's (instability) condition,
to a compressible heat-conducting viscous flow without heat conductivity in the
presence of a uniform gravitational field in a three-dimensional bounded
domain. We show that the equilibrium state is linearly unstable by a modified
variational method. Then, based on the constructed linearly unstable solutions
and a local well-posedness result of classical solutions to the original
nonlinear problem, we further construct the initial data of linearly unstable
solutions to be the one of the original nonlinear problem, and establish an
appropriate energy estimate of Gronwall-type. With the help of the established
energy estimate, we finally show that the equilibrium state is nonlinearly
unstable in the sense of Hadamard by a careful bootstrap instability argument.
