  We emphasise the importance of the gas entropy in studying the evolution of
cluster gas evolving under the influence of radiative cooling. On this basis,
we develop an analytical model for this evolution. We then show that the
assumptions needed for such a model are consistent with a numerical solution of
the same equations. We postulate that the passive cooling phase ends when the
central gas temperature falls to very low values. It follows a phase during
which an unspecified mechanism heats the cluster gas. We show that in such a
scenario the small number of clusters containing gas with temperatures below
about 1 keV is simply a consequence of the radiative cooling.
