  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.
