A Quench in cable-in-conduit (CIC) conductors is often initiated by a disturbance such as strand motion that generates a highly localized normal zone in a strand or a few strands of the CIC conductors. The localized normal zone causes current and heat transfer between a disturbed strand and neighboring strands. Electrical and thermal contact characteristics between strands thus have an effect on the transient stability of the CIC conductors. In this paper the effect of contact characteristics between strands on the CIC conductor stability is presented based on the measured heat transfer characteristics of supercritical helium (SHe) for the local heating. The quench and recovery processes of the strands for the abrupt and highly localized disturbance are analyzed at the boundary between quench and recovery.