ISO data taken with the long-wavelength imaging photo-polarimeter ISOPHOT are presented of 18 pre-stellar cores at three far-infrared wavelengths - 90, 170 and 200 microns. Most of the cores are detected clearly at 170 and 200 but only one is detected strongly at 90 microns, indicating that mostly they are very cold, with typical temperatures of only 10-20K. Colour temperature images are constructed for each of the cores. Most of the cores are seen to be either isothermal, or to have associated temperature gradients from the core centres to their edges, with all except one being cooler at the centre. We compare the data with previous ISOCAM absorption data and calculate the energy balance for those cores in common between the two samples. We find that the energy radiated by each core in the far-IR is similar to that absorbed at shorter wavelengths. Hence there is no evidence for a central heating source in any of the cores - even those for which previous evidence for core contraction exists. This is all consistent with external heating of the cores by the local interstellar radiation field, confirming their pre-stellar nature.