Spiral galaxies with very cold global dust temperatures may be unique cases of normal galaxies caught in an extremely quiescent phase of their evolution. Gas rich but dormant, they are just as critical to understand as the starbursts if one is to gain unbiased insight into galaxy evolution processes. However, these galaxies are quite rare and little is known about them. We propose to study with ISO a subset of the 47 coldest galaxies (FIR colors: 0.1 < r(60,100) = f(60um)/f(100um) < 0.25, or roughly 19 < T < 26K) found among over 60,000 galaxies in the IRAS Faint Source Catalog (FSC). With FIR colors comparable to that of Galactic cirrus [r(60,100) 0.21], and small ratios of L(FIR)/L(B) and of L(FIR)/M(HI), these galaxies have a very low rate of current star formation. Most of them are spirals of types Sab to Scd, with normal optical luminosities, suggesting more vigorous star formation in the past; they also possess normal amounts of HI gas, potential raw material for renewed star formation. Notwithstanding this HI however, they may well lack the molecular gas reserves that are the immediate fuel for star formation, and may thus have been forced into a prolonged rather than a temporary quiescence, possibly preparing their transformation into lenticulars. To test this hypothesis we propose ISOPHOT broad-band photometry at 25, 160 and 200 um, and ISOCAM imaging photometry at 12 um, for a sample of 16 galaxies, and LWS measurements of the [CII] line at 158um for a subsample of 8. We also propose ISOPHOT photometry at 60 and 100um on 2 or 4 coldest galaxies with low Galactic latitudes to confirm IRAS colors. The proposed ISO photometry is crucial to estimating the FIR luminosity, the temperature and spatial distribution, and the total mass of the dust in these galaxies; if their continuum spectrum, especially beyond 100um, is indistinguishable from that of atomic cirrus, the temporary quiescence hypothesis will be severely challenged. The proposed ISO observations on [CII] would provide another test distinguishing between atomic cirrus and molecular cloud emission by comparison with other ISO data.