Ratio h(R_core)/h(0) (top figure), the heating rate h(R_core) at the cores’ edge (central figure), and the heating rate in the core center h(0) (bottom figure) as a function of the central pressure in the filaments for the three different assumption of the external pressure p_ext. For comparison also the corresponding dust temperatures of a simplified dust model are shown. For sake of clarity the values obtained for cores in spherical filaments which are pressurized by the same external pressure p_ext are given as solid black curves. The values are labelled with the considered extinction values A_V through the filaments’ center.