Hot DM refers to particles, such as neutrinos, that were moving at nearly the speed of light at redshift z ~ 106 (or time t ~ 1 yr), when the temperature T ~ 3 x 102 eV and the cosmic horizon first encompassed 1012 M, the amount of dark matter contained in the halo of a large galaxy like the Milky Way. Hot DM particles must also be still in thermal equilibrium after the last phase transition in the hot early universe, the QCD confinement transition, which presumably took place at TQCD 102 MeV. Hot DM particles have a cosmological number density roughly comparable to that of the microwave background photons, which (as we will see shortly) implies an upper bound to their mass of a few tens of eV. This then implies that free streaming of these relativistic particles destroys any fluctuations smaller than supercluster size, ~ 1015 M.
The ``hot,'' ``warm,'' ``cold'' DM terminology was introduced in 1983 [5, 6]. Warm DM particles interact much more weakly than neutrinos. They decouple (i.e., their mean free path first exceeds the horizon size) at T >> TQCD, and are not heated by the subsequent annihilation of hadronic species. Consequently their number density is roughly an order of magnitude lower, and their mass an order of magnitude higher, than hot DM particles. Fluctuations corresponding to sufficiently large galaxy halos, 1011 M, could then survive free streaming. In theories of local supersymmetry broken at ~ 106 GeV, gravitinos could be DM of the warm variety [7, 8, 9]. Other warm dark matter candidates are also possible, of course, such as right-handed neutrinos . Warm DM does not fit the observations if m = 1 , but for low m some have suggested that it may be worth reconsidering, to avoid some possible problems of Cold DM [12, 13]. However, the cutoff in the power spectrum P(k) at large k implied by WDM will also inhibit the formation of small dark matter halos at high redshift. But such small halos are presumably where the first stars form, which produce metals rather uniformly throughout the early universe as indicated by observations of the Lyman forest (neutral hydrogen clouds seen in absorption in quasar spectra).
Cold DM consists of particles for which free streaming is of no cosmological importance. Two different sorts of cold DM consisting of elementary particles have been proposed, heavy thermal remnants of annihilation such as supersymmetric neutralinos, and a cold Bose condensate such as axions. A universe where the matter is mostly cold DM and there is a large cosmological constant looks very much like the one astronomers actually observe, and this low-m CDM model  is the current favorite model for structure formation in the universe [15, 16, 17].