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We estimate the dust temperatures of the clumps in the ρ Oph main cloud taking into account the 3D geometry of the region, and external heating from the interstellar radiation field and from HD 147879, a nearby luminous B2V star, which is believed to dominate the radiation field in the region. We find that the regions where pre‐stellar cores are observed (i.e. at optical visual extinctions &gt;7 mag) are colder than  ∼10 –11   K . These dust temperatures are smaller than those which previous studies of the same region have assumed. We use the new dust temperatures to estimate the masses of the pre‐stellar cores in the ρ Oph main cloud from millimetre observations, and we find core masses that are larger than previous estimates by a factor of  ∼2 –3 . This affects the core mass function (CMF) of the region; we find that the mass at which the core mass spectrum steepens from a slope α∼ 1.5 to a slope α∼ 2.5 has moved from ∼0.5 to  ∼1 M ⊙  . In contrast with the CMF in other star‐forming regions (e.g. Orion), there is no indication for a turnover down to the completeness limit  (∼0.2 M ⊙ ) , but the CMF may flatten at around  ∼0.4 M ⊙  .  We generalize our results to the pre‐stellar cores in Taurus and in Orion. In Taurus, the ambient radiation field heating the pre‐stellar cores is believed to be weaker than that in ρ Oph. Hence, the dust temperatures of the cores in Taurus are expected to be below  ∼10 –11   K . In Orion, the radiation field is believed to be 10 3  times stronger than the standard interstellar radiation field. Based on this assumption, we estimate that the dust temperatures of the pre‐stellar cores in Orion are around  ∼20 –30   K .

The dust temperatures of the pre‐stellar cores in the ρ Oph main cloud and in other star‐forming regions: consequences for the core mass function