  We present a compilation of PRONAOS-based results concerning the temperature
dependence of the dust submillimeter spectral index, including data from
Galactic cirrus, star-forming regions, dust associated to a young stellar
object, and a spiral galaxy. We observe large variations of the spectral index
(from 0.8 to 2.4) in a wide range of temperatures (11 to 80 K). These spectral
index variations follow a hyperbolic-shaped function of the temperature, high
spectral indices (1.6-2.4) being observed in cold regions (11-20 K) while low
indices (0.8-1.6) are observed in warm regions (35-80 K). Three distinct
effects may play a role in this temperature dependence: one is that the grain
sizes change in dense environments, another is that the chemical composition of
the grains is not the same in different environments, a third one is that there
is an intrinsic dependence of the dust spectral index on the temperature due to
quantum processes. This last effect is backed up by laboratory measurements and
could be the dominant one.
