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.
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