Tri-axial cable has been rapidly developed recently because of the advantages such as more compact structure, small leakage field, and low heat and AC losses. One the other hand, it causes an inherent imbalanced three-phase currents distribution due to the different radii of concentric layers. In our previous research, it is demonstrated that a proposed tri-axial cable composed of two longitudinal sections with adjusted twist pitches can transmit balanced three-phase currents. However, before the cable can be installed in a real grid, the heat reliability of the cable in steady-state operation and fault condition should be ensured. The heat balance calculation of the tri-axial cable in steady state under the balanced current distribution allows us to estimate thermal parameters of the cable such as inlet and outlet temperatures, pressure drop and operation temperature. When a phase current suddenly changes under fault conditions, the remaining phase currents become large because of mutual inductances between fault and sound phases. Simulation of the typical fault suggests the copper stabilizer amount on the HTS tape for stability and safety. It is found that copper of 2 mm in thickness keeps the cable temperature under 110 K.Index Terms-Fault current, HTS power cable, stabilizer, triaxial cable.