  Within the framework of the DustPedia project we investigate the properties
of cosmic dust and its interaction with the stellar radiation (originating from
different stellar populations) for 814 galaxies in the nearby Universe, all
observed by the Herschel Space Observatory. We take advantage of the widely
used galaxy SED fitting code CIGALE, properly adapted to include the
state-of-the-art dust model THEMIS. Using the DustPedia photometry we determine
the physical properties of the galaxies, such as, the dust and stellar mass,
the star-formation rate, the bolometric luminosity as well as the unattenuated
and the absorbed by dust stellar light, for both the old (> 200 Myr) and young
(<= 200 Myr) stellar populations. We show how the mass of stars, dust, and
atomic gas, as well as the star-formation rate and the dust temperature vary
between galaxies of different morphologies and provide recipes to estimate
these parameters given their Hubble stage (T). We find a mild correlation
between the mass fraction of the small a-C(:H) grains with the specific
star-formation rate. On average, young stars are very efficient in heating the
dust, with absorption fractions reaching as high as ~77% of the total,
unattenuated luminosity of this population. On the other hand, the maximum
absorption fraction of old stars is ~24%. Dust heating in early-type galaxies
is mainly due to old stars, up to a level of ~90%. Young stars progressively
contribute more for `typical' spiral galaxies and they become the dominant
source of dust heating for Sm type and irregular galaxies, donating up to ~60%
of their luminosity to this purpose. Finally, we find a strong correlation of
the dust heating fraction by young stars with morphology and the specific
star-formation rate.
