Thermal equilibrium of molecular clouds in cooling flow clusters

In many clusters of galaxies there is evidence for cooling flows in the cen tral regions. The ultimate fate of the gas which cools is still unknown. A possibility is that a fraction of the gas forms cold molecular clouds. We i nvestigate the minimum temperature which can be reached by clouds in coolin g flows by computing the cooling function due to H-2, HD and CO molecules. As an example, we determine the minimum temperature achievable by clouds in the cooling flows of the Centaurus, Hydra and PKS 0745-191 clusters. Our r esults suggest that clouds can reach very low temperatures less than simila r to 10K - which would explain the non-detection of CO in these clusters.