The dense hot intracluster gas in the central 100-200 kpc of most clusters of galaxies is cooling on a timescale of less than 10 billion yrs leading to cooling flows at rates of 10s to 100s Msun /yr. This must cause the accumulation of 1e11 to 1e13 Msun of cooled material around the central cluster galaxies. Absorption seen in X-ray spectra indicates that much of this cooled matter remains as cold gas, probably in the form of very cold clouds. Part of the cooled product of flows may form stars, which must be of low mass in order that optical magnitudes are not exceeded. We propose here to search for line radiation from the cold gas clouds at [OI]63mu and [SiII]34.8mu which is predicted to emerge from throughout the cooling flow. The discovery of such extended infrared radiation would open up this new component of the intracluster medium for detailed study. It has widespread implications for the formation of the most massive galaxies and for baryonic dark matter, as well as the nature of the whole intracluster medium, which may be multiphase. The numbers of clouds in the inner few kpc of a massive flow are so high that cloud-cloud collisions and aggregation occur, leading to optical nebulosities and massive star formation in some central cluster galaxies. We further propose to observe this region in such galaxies, where dust, possibly formed in the dense clouds, may obscure much of the action in the optical band. The objects proposed for here are the most massive, nearby cooling flows and are the most massive and extensive regions of cold gas at low redshifts. ISO can provide vital direct information on the nature and evolution of this newly-recognized major component of the Universe.