The temperature and density structure of molecular cloud cores are the most important physical quantities that determine the course of the protostellar collapse and the properties of the stars they form. Nevertheless, density profiles often rely either on the simplifying assumption of isothermality or on observationally poorly constrained model temperature profiles. With the aim of better constraining the initial physical conditions in molecular cloud cores at the onset of protostellar collapse, we initiated the Guaranteed Time Key Project (GTKP) The Earliest Phases of Star Formation (EPoS) with the Herschel satellite. This paper gives an overview of the low-mass sources in the EPoS project, including all observations, the analysis method, and the initial results of the survey. We study the thermal dust emission of 12 previously well-characterized, isolated, nearby globules using FIR and submm continuum maps at up to eight wavelengths between 100 micron and 1.2 mm. Our sample contains both globules with starless cores and embedded protostars at different early evolutionary stages. The dust emission maps are used to extract spatially resolved SEDs, which are then fit independently with modified blackbody curves to obtain line-of-sight-averaged dust temperature and column density maps. We find that the thermal structure of all globules is dominated by external heating from the interstellar radiation field and moderate shielding by thin extended halos. All globules have warm outer envelopes (14-20 K) and colder dense interiors (8-12 K). The protostars embedded in some of the globules raise the local temperature of the dense cores only within radii out to about 5000 AU, but do not significantly affect the overall thermal balance of the globules.
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