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In order to design a high temperature superconducting (HTS) winding for the fault current limiter (FCL), the resistance and the temperature of the winding should be calculated quantitatively under the over-current caused by fault condition. In this paper, a transient analysis is performed to estimate the resistance development and the temperature rise of coated conductor (CC) under AC over-current. A one-dimensional thermal conduction model with an electrical circuit model is developed for the solenoid coil configuration at 65 K cooling condition. All the composite materials except the buffer layer in CC are considered in the model. Two kinds of stabilizer materials (copper/stainless steel) are considered to investigate the current limitation of CC. The simulation results are compared with the experimental data of the commercial CC. The effect of Ag and solder layer on the simulation result are revealed for CC.