[en] The Muon-to-Electron conversion experiment (Mu2e), under development at Fermilab, seeks to detect direct muon to electron conversion to provide evidence for a process violating muon and electron lepton number conservation that cannot be explained by the Standard Model of particle physics. The required magnetic field is produced by a series of superconducting solenoids of various apertures and lengths. This paper describes the conceptual design of the 5 T, 4 m long solenoid cold mass with 1.67 m bore with the emphasis on the magnetic, radiation and thermal analyses.