When 10 kV three-core cable needs to load emergency loads in failure or maintenance, the time the cable can resist the over-load before the temperature of cable conductor reaches the maximum temperature is the major and urgent issue for power department. Therefore, taking the 10 kV three-core cables laid in air as research object, a transient thermal circuit model of cable and air media is established, and the heating time constant of 10 kV three-core cables is calculated by simplifying it into a first-order RC transient thermal circuit model. In addition, the emergency time calculation formula for three-core cable laid in air and the emergency heating experiment for cable laid in air under different initial load are put forward. By comparing the empirical data and theoretical data, the reliability of the proposed model and emergency time calculation formula is successfully proved, which provides an important reference to electricity load distribution under emergency and the control of time in cable maintenance.