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.