  A systematic study of the linear thermal stability of a medium subject to
cooling, self-gravity and thermal conduction is carried out for the case when
the unperturbed state is subject to global cooling and expansion. A general,
recursive WKB solution for the perturbation problem is obtained which can be
applied to a large variety of situations in which there is a separation of
time-scales for the different physical processes. Solutions are explicitly
given and discussed for the case when sound propagation and/or self-gravity are
the fastest processes, with cooling, expansion and thermal conduction operating
on slower time-scales. A brief discussion is also added for the solutions in
the cases in which cooling or conduction operate on the fastest time-scale. The
general WKB solution obtained in this paper permits solving the problem of the
effect of thermal conduction and self-gravity on the thermal stability of a
globally cooling and expanding medium. As a result of the analysis, the
critical wavelength (often called Field length) above which cooling makes the
perturbations unstable against the action of thermal conduction is generalized
to the case of an unperturbed background with net cooling. As an astrophysical
application, the generalized Field length is calculated for a hot (10^4 - 10^8
K), optically thin medium (as pertains, for instance, for the hot interstellar
medium of SNRs or superbubbles) using a realistic cooling function and
including a weak magnetic field. The stability domains are compared with the
predictions made on the basis of models for which the background is in thermal
equilibrium. The instability domain of the sound waves, in particular, is seen
to be much larger in the case with net global cooling.
