We estimate the dust temperatures of the clumps in the \rho Oph main cloud taking into account the 3D geometry of the region , and external heating from the interstellar radiation field and from HD147879 , a nearby luminous B2V star , which is believed to dominate the radiation field in the region .
We find that the regions where prestellar cores are observed ( i.e .
at optical visual extinctions > 7 mag ) are colder than \sim 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 prestellar cores in the \rho Oph main cloud from mm observations , and we find core masses that are larger than previous estimates by a factor of \sim 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 \alpha \sim 1.5 to a slope \alpha \sim 2.5 has moved from \sim 0.5 M _ { \sun } to \sim 1 M _ { \sun } .
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 ( \sim 0.2 M _ { \sun } ) , but the CMF may flatten at around \sim 0.4 M _ { \sun } .

We generalize our results to the prestellar cores in Taurus and in Orion .
In Taurus the ambient radiation field heating the prestellar cores is believed to be weaker than than that in \rho Oph .
Hence , the dust temperatures of the cores in Taurus are expected to be below \sim 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 prestellar cores in Orion are around \sim 20 - 30 K .