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We present a compilation of PRONAOS-based results concerning the temperaturedependence of the dust submillimeter spectral index, including data fromGalactic cirrus, star-forming regions, dust associated to a young stellarobject, 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 spectralindex variations follow a hyperbolic-shaped function of the temperature, highspectral indices (1.6-2.4) being observed in cold regions (11-20 K) while lowindices (0.8-1.6) are observed in warm regions (35-80 K). Three distincteffects may play a role in this temperature dependence: one is that the grainsizes change in dense environments, another is that the chemical composition ofthe grains is not the same in different environments, a third one is that thereis an intrinsic dependence of the dust spectral index on the temperature due toquantum processes. This last effect is backed up by laboratory measurements andcould be the dominant one.  We also briefly present a joint analysis of WMAP dust data together withCOBE/DIRBE and COBE/FIRAS data.Comment: 4 pages, 2 figures, contribution to the proceedings of the  Cologne-Bonn-Zermatt conference, held in Zermatt, Switzerland, Sept. 2003,  eds: S. Pfalzner, C. Kramer, C. Straubmeier, and A. Heithausen,  Springer-Verla

New Insights on the Thermal Dust from the Far-Infrared to the Centimeter