A very simple but general criterion for local thermal instability in dynamical sytems is derived. The background flow may be time-dependent. The instability criterion is very similar to the classical Field result, except that the cooling function L is replace by L/T, whre T is the temperature. Previous results in the literature are special cases of our result. A third-order differential equation for the evolution of small-wavelength radial perturbations in spherical systems is derived. With self-gravity, it is the exact equation that would result for the evolution of perturbations in simple matter-dominated Friedmann cosmologies (or any homogeneous volume change) subject to external heating and cooling. The scale factor is determined by the unperturbed velocity flow. The equation is solved by WKBJ techniques, allowing acoustical and condensational modes to be treated on an equal footing. Transport processes are not considered here. Self-gravity and fragmentation are briefly discussed.