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Reduction of the cooling cost and the securing of thermal stability are important problems to put HTS power cables to practical use. It is in particular very important in an HTS cable design to estimate the temperature rise by the AC loss and the over current precisely. The detailed behavior of the ac loss and the temperature distribution in a co-axial multi-layered BSCCO HTS power cable are analyzed by the magneto-thermal coupled method considering the temperature dependence of the critical current density and the Cu electrical resistance. Moreover, the temperature rise by the ac loss and the ohmic loss in each layer under the over current is calculated and the cooling necessity from the inside of a Cu former is examined.