We present Herschel/PACS 100 and 160 μm integrated photometry for the 323 galaxies in the Herschel Reference Survey (HRS), a K-band, volume-limited sample of galaxies in the local Universe. Once combined with the Herschel/SPIRE observations already available, these data make the HRS the largest representative sample of nearby galaxies with homogeneous coverage across the 100-500 μm wavelength range. In this paper, we take advantage of this unique data set to investigate the properties and shape of the far-infrared/submillimetre spectral energy distribution in nearby galaxies. We show that, in the stellar mass range covered by the HRS (8 ≤ log (M*/M⊙) ≤ 12), the far-infrared/submillimetre colours are inconsistent with a single modified blackbody having the same dust emissivity index β for all galaxies. In particular, either β decreases or multiple temperature components are needed, when moving from metal-rich/gas-poor to metal-poor/gas-rich galaxies. We thus investigate how the dust temperature and mass obtained from a single modified blackbody depend on the assumptions made on β. We show that, while the correlations between dust temperature, galaxy structure and star formation rate are strongly model dependent, the dust mass scaling relations are much more reliable, and variations of β only change the strength of the observed trends. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.