Gamma-ray bursts (GRBs) have been proposed as a tool for studying star formation in the Universe, so it is crucial to investigate whether their host galaxies and immediate environments are in any way special compared with other star-forming galaxies. Here we present spatially resolved maps of dust emission of the host galaxyof the closest known GRB 980425 at z = 0.0085 using our new high-resolution observations from Herschel, Atacama Pathfinder Experiment (APEX), Atacama Large Millimeter Array (ALMA) and Australia Telescope Compact Array (ATCA). We modelled the spectral energy distributions of the host and of the star-forming region displaying the Wolf-Rayet signatures in the spectrum (WR region), located 800 pc from the GRB position. The host is characterised by low dust content and a high fraction of UV-visible star formation, similar to other dwarf galaxies. These galaxies are abundant in the local universe, so it is not surprising to find a GRB in one of them, assuming the correspondence between the GRB rate and star formation. The WR region contributes substantially to the host emission at the far-infrared, millimetre, and radio wavelengths and we propose that this is a consequence of its high gas density. If dense environments are also found close to the positions of other GRBs, then the ISM density should also be considered, along with metallicity, an important factor influencing whether a given stellar population can produce a GRB. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. Reduced images as FITS files are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/562/A70.