Ferromagnetic interlayer coupling through a semiconducting spacer has been studied in epitaxial layered structures Fe/EuS/Fe(001). The coupling strength has been determined as a function of temperature and interlayer thickness using magneto-optical Kerr effect magnetometry. A strong rise of the coupling strength with increasing temperature has been observed in the temperature range, where EuS is paramagnetic. The observations match the theoretical description of interlayer exchange coupling between two metallic layers mediated by the electronic states in a semiconductor. Near the Curie temperature of EuS, long-range ferromagnetic coupling is observed, that is related to ferromagnetic order inside the EuS layer.