Context. RCW 120 is a well-studied, nearby Galactic H II region with ongoing star formation in its surroundings. Previous work has shown that it displays a bubble morphology at mid-infrared wavelengths, and has a massive layer of collected neutral material seen at sub-mm wavelengths. Given the well-defined photo-dissociation region (PDR) boundary and collected layer, it is an excellent laboratory to study the “collect and collapse” process of triggered star formation. Using Herschel Space Observatory data at 100, 160, 250, 350, and 500 μm, in combination with Spitzer and APEX-LABOCA data, we can for the first time map the entire spectral energy distribution of an H II region at high angular resolution.Aims. We seek a better understanding of RCW 120 and its local environment by analysing its dust temperature distribution. Additionally, we wish to understand how the dust emissivity index, β, is related to the dust temperature.Methods. We determine dust temperatures in selected regions of the RCW 120 field by fitting their spectral energy distribution (SED), derived using aperture photometry. Additionally, we fit the SED extracted from a grid of positions to create a temperature map.Results. We find a gradient in dust temperature, ranging from ≳30 K in the interior of RCW 120, to ~20 K for the material collected in the PDR, to ~10 K toward local infrared dark clouds and cold filaments. There is an additional, hotter (~100 K) component to the dust emission that we do not investigate here. Our results suggest that RCW 120 is in the process of destroying the PDR delineating its bubble morphology. The leaked radiation from its interior may influence the creation of the next generation of stars. We find support for an anti-correlation between the fitted temperature and β, in rough agreement with what has been found previously. The extended wavelength coverage of the Herschel data greatly increases the reliability of this result.