Grain boundary segregation energies of solute elements play a decisive role for alloy design. So far, the temperature dependence of these energies has been neglected in first principles modelling, whereas in experimental assessments, they received a lot of attention. We compute the free energies of segregation from first principles for typical alloying elements and find that the vibrational contribution to segregation energies is substantial and affects solute enrichment. Our results clarify the origin of the entropy of segregation, which has been discussed so far only on experimental basis.