We gather infrared (IR) photometric data from 8 to 500 microns (Spitzer, WISE, IRAS and Herschel) for all of the HRS galaxies. Draine & Li (2007) models are fit to the data from which the stellar contribution has been carefully removed. We find that our photometric coverage is sufficient to constrain all of the models parameters and that a strong constraint on the 20-60 microns range is mandatory to estimate the relative contribution of the photo-dissociation regions to the IR SED. The SED models tend to systematically under-estimate the observed 500 microns flux densities, especially for low mass systems. We provide the output parameters for all of the galaxies: the minimum intensity of the interstellar radiation field (ISRF), the fraction of PAH, the relative contribution of PDR and evolved stellar population to the dust heating, the $M_{dust}$ and the $L_{IR}$. For a subsample of gas-rich galaxies, we analyze the relations between these parameters and the integrated properties of galaxies, such as $M_*$, SFR, metallicity, H$alpha$ and H-band surface brightness, and the FUV attenuation. A good correlation between the fraction of PAH and the metallicity is found implying a weakening of the PAH emission in galaxies with low metallicities. The intensity of the IRSF and the H-band and H$alpha$ surface brightnesses are correlated, suggesting that the diffuse dust component is heated by both the young stars in star forming regions and the diffuse evolved population. We use these results to provide a new set of IR templates calibrated with Herschel observations on nearby galaxies and a mean SED template to provide the z=0 reference for cosmological studies. For the same purpose, we put our sample on the SFR-$M_*$ diagram. The templates are compared to the most popular IR SED libraries, enlightening a large discrepancy between all of them in the 20-100 microns range.
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