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A current lead with kA capacity and small AC loss is being developed for use in superconducting current limiting devices cooled with liquid helium. A gas-cooled type current lead using Bi-based oxide superconducting bulk materials was examined to clarify the effects of the current lead geometry and the use of multiple current leads. This paper presents the results of experiments and numerical simulations based on the finite element method taking consideration of nonuniform transport current distribution among multiple current leads connected in parallel. The simulations are performed to investigate the relationship between the geometry of current leads and the amount of heat flow into a cryostat. In the simulations, the AC loss caused by both mutual and self-induced magnetic fields of multiple current leads is taken into account. The influence of AC loss, the joule heat generated by the contact resistance at joints of NbTi/CuNi multi-strand cables and the HTS bars, and the return passage for gas on the operating characteristics of the HTS current leads are evaluated.