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NbTi cable-in-conduit-conductors (CICC's) are employed to fabricate plasma fusion experimental apparatuses. NbTi is a preferable material in terms of low cost and good manufacturability. In contrast, it shows lower stability compared to materials for high magnetic field applications, e. g. Nb3Sn, due to its small critical temperature. A characteristic feature in NbTi multi-strand cable is so called avalanche-like quench, which is specific instability in a parallel electric circuit consisting of superconducting lines. To evaluate stability of a NbTi cable, we employed induced-current methods. Current is increased and decreased by constant voltage source, i. e. magnetic flux change produced by the bias magnet. We evaluated the quenches and equilibrium condition between heat generation due to flux flow voltage and heat transfer to surroundings at critical current. A parameter of experiment was a ramp rate of the bias field that corresponds to electric field in the cable. Of course, the cable was stable with smaller electric field and/or critical current. To survey the influence of heat dissipation during this equilibrium, we changed the surrounding mediums; those are liquid helium, frozen ethanol and ice. Ice is the material with large thermal conductivity, therefore this results in good stability of the cable.