In particle accelerators, the beam screen is the device responsible for shielding the superconducting magnets from the synchrotron radiation emitted by the orbiting charged particles. It is crucial to have a low value of the coupling impedance between the beam and the surrounding beam screen to avoid collective instabilities of the charged beams. To achieve this at typical operating temperatures, 40–60K, of the CERN Future Circular hadron Collider, a hybrid coating, made of alternated segments of RE(=Y, Gd, Eu)BaCuO high-temperature superconductor and Cu, is proposed for the beam screen. Previous studies have shown that such an arrangement can exhibit low surface impedance and, therefore, low beam-coupling impedance, while not hindering the magnetic field quality in the vacuum chamber, which is another relevant factor for accelerator performance. In this work, we propose a design for the beam screen coating and explore its response to the electromagnetic conditions of the FCC-hh. The field disturbance produced by the coating with the high-temperature superconductor is evaluated by means of H-formulation finite elements numerical analysis, considering properties of commercially available HTS coated conductors, such as anisotropy,  dependence on the external magnetic field, and flux creep. The coating response to ramping dipole and quadrupole fields is examined, as well as hysteresis effects and creep at constant field over a sustained period of time. Finally, the effects on the field quality experienced by the beam caused by a possible misalignment between the superconducting magnets and the beam screen are investigated.