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Limiting operation of a superconducting fault current limiter (SFCL) depends on multilateral interaction effects among the three critical delimited superconductivity parameters, namely, current, temperature, and magnetic field, as well as dependent impedance in addition to other specifications in the external power system. As such, considerable efforts are now being invested in developing strategies for the design and fabrication of new SFCLs involving an interplay or synergy between electrical conductivity, magnetic, and thermal properties. This paper introduces a comprehensive approach for a parallel processing of electromagnetic and thermal transient analysis, accounting for load current and recloser coordination, in an exemplary open-core magnetic-shield-type SFCL. Decisively, this requires accurate, yet efficient, high-temperature superconductor (HTS) modeling, which is yielded by a detailed localized E-J power law approach combining the different aspects of HTS. This leads to qualified results via finite-element analysis for magnetic field and temperature distributions in prefault, fault, and postfault states. Furthermore, the relation between recloser operation and SFCL intrinsic specifications such as quench and recovery time is studied. The transient analysis of the leakage flux densities and the corresponding radial and axial components of electromagnetic forces on the windings of the SFCL are further contributions of this paper. Thermal stress resulted from thermal expansion of HTS tube is another object of this study.