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We present 1.25 mm continuum data for a southern galaxy sample selected from the IRAS PSC and complete to S_60=2 Jy. Two thirds of the galaxies have been detected and significant limits on the remaining objects have been set. We find, on a statistical basis, indications that the dust emission in these galaxies is somewhat more centrally concentrated than that of the optical light, possibly tracing a higher metal content in the inner galactic regions. This result also allows to estimate the aperture corrections to the millimetric data. The latter, together with IRAS photometric data, have been used to compare the broad-band FIR/mm spectra with a simple dust model. According to their far-IR/mm spectrum, the sample galaxies show a dichothomy: almost half of the objects, those displaying bright 25-60um fluxes ascribed to warm dust residing in 'starburst' regions, are characterized by higher values of the bolometric (optical + FIR) luminosity, of the dust-to-gas mass ratio, of the dust optical depths and of the overall extinction. A complementary class of objects dominated by cold dust ('cirrus') shows opposite trends. Because of the favourable observational setup, selection wavelength and completeness, we believe these data provide an exhaustive and unbiased view of dust properties in spiral galaxies

1.25-mm observations of a complete sample of IRAS galaxies -- II. Dust properties