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(Abridged) We present the dust properties of 125 bright Herschel galaxiesselected from the z-GAL survey. The large instantaneous bandwidth of NOEMAprovides an exquisite sampling of the underlying dust continuum emission at 2and 3 mm in the observed frame, with flux densities in at least four side bandsfor each source. Together with the available Herschel 250, 350, and 500 micronand SCUBA-2 850 micron flux densities, the spectral energy distribution of eachsource can be analyzed from the far-infrared to the millimeter, with a finesampling of the Rayleigh-Jeans tail. This wealth of data provides a solid basisto derive robust dust properties, in particular the dust emissivity index,beta, and the dust temperature, T(dust). In order to demonstrate our ability toconstrain the dust properties, we used a flux-generated mock catalog andanalyzed the results under the assumption of an optically thin and opticallythick modified black body emission. For the z-GAL sources, we report a range ofdust emissivities with beta ~ 1.5 - 3 estimated up to high precision withrelative uncertainties that vary in the range 7% - 15%, and an average of 2.2+/- 0.3. We find dust temperatures varying from 20 to 50 K with an average ofT(dust) ~ 30 K for the optically thin case and ~38 K in the optically thickcase. For all the sources, we estimate the dust masses and apparent infraredluminosities (based on the optically thin approach). An inverse correlation isfound between T(dust) and beta, which is similar to what is seen in the localUniverse. Finally, we report an increasing trend in the dust temperature as afunction of redshift at a rate of 6.5 +/- 0.5 K/z for this 500 micron-selectedsample. Based on this study, future prospects are outlined to further explorethe evolution of dust temperature across cosmic time.

z-GAL -- A NOEMA spectroscopic redshift survey of bright Herschel galaxies: [II] Dust properties