We derive the temperature dependence of the electronic quasiparticle spectrum of the ferromagnetic semiconductor EuS. The study is based on a d-f exchange model, whose ``free'' part contains as important model parameters the Bloch energies ${\ensuremath{\epsilon}}_{m}$(k). These quantities are determined by a self-consistent, spin-polarized band-structure calculation within the framework of density-functional theory, thereby incorporating all interactions which are not explicitly taken into account by the d-f model. This is approximately solved by a many-body procedure, which treats spin-exchange processes between localized 4f moments and itinerant conduction electrons with special care. The method is exact at T=0. We discuss in detail the temperature dependence of the quasiparticle density of states and of the quasiparticle band structure for the first five unoccupied conduction bands, which are mainly of 5d type.