SPES (Selective Production of Exotic Species) is a second generation facility for the production of radioactive ion beams that is going to be commissioned at the Laboratori Nazionali di Legnaro of INFN at Legnaro, Padua, Italy. Radioactive neutron-rich isotopes are expected to be produced by nuclear fission induced by a 40 MeV, 200 μA primary proton beam impinging on a 238UCx target. The expected reaction rate is about 1013 fission/s. Radioactive ion beams are produced using the isotope separation on-line technique. The production of such an amount of radioactive species raises radiological issues throughout the life cycle of the facility. A study of the radioactive contamination of the components of the radioactive ion beam line is performed with the FLUKA Monte Carlo simulation code, under realistic hypotheses for the produced isobaric beams. The present results complete previous studies focused on the radiological impact of the production target irradiation, the residual activation of the primary proton beam line and the radioactive contamination of the ion source complex. The overall ambient dose equivalent rate due to the different radiation sources is calculated at several positions inside the production bunker and at different times after a typical one-year operating period of the facility with the 238UCx target at full power. The obtained results and the developed methodology provide the guidelines and the needed tools to plan ordinary and extraordinary interventions as well as final decommissioning of the SPES facility.