System for variably controlling engine-on line in consideration of cooling after fatc engine is turned on

A system for variably controlling an engine-on line after a full automatic temperature control (FATC) engine is turned on, the system comprising:

• a prediction degree calculation unit configured to predict a degree to which a temperature of a coolant at a current point after the engine is turned off reaches a target temperature at which the engine is turned on, by a request of a full automatic temperature control (FATC);
• a factor determination unit configured to:
• set reference ranges divided based on an extent that the temperature is close to the target temperature, and determine a factor value for each reference range of the reference ranges so that a predetermined existing engine-on line or a predetermined existing engine-off line is varied by a required power;
• and
• an engine on/off line determination unit configured to determine a corrected engine-on line or a corrected engine-off line by calculating the existing engine-on line or the existing engine-off line and the factor value in the reference ranges in which a calculation value calculated by the prediction degree calculation unit is positioned.