We present here a compilation of PRONAOS-based results concerning the temperature dependence of the dust submillimeter spectral index , including data from Galactic cirrus , star-forming regions and a circumstellar envelope . We observe large variations of the spectral index ( from 0.8 to 2.4 ) in a wide range of temperatures ( 12 to 80 K ) . These spectral index variations follow a hyperbolic-shaped function of the temperature , large spectral indices ( 1.5-2.4 ) being observed in cold regions ( 12-20 K ) while small indices ( 0.8-1.6 ) are observed in warm regions ( 35-80 K ) . Three interpretations are proposed : one is that the grain sizes change in warm and rather 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 .