We present Herschel/PACS 100 and 160 mu m 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 mu m 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 less than or similar to log (M-*/M-circle dot) less than or similar to 12), the far-infrared/submillimetre colours are inconsistent with a single modified blackbody having the same dust emissivity index beta for all galaxies. In particular, either beta 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 beta. 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 beta only change the strength of the observed trends.