An engine automatic start stop control apparatus for controlling an engine of a vehicle to be automatically stopped or started in response to driving conditions of a vehicle, which is equipped with a manual transmission, an automatic transmission or a continuously variable transmission (CVT). The apparatus makes a determination whether or not to allow stop (or idle stop) of the engine in consideration of a relationship between outside air temperature and engine water temperature. This prevents a catalyst from being deteriorated in performance as a result of a temperature reduction of the catalyst occurs when the engine idling is carelessly stopped. Thus, it is possible to effectively reduce discharge gas of the vehicle. The outside air temperature can be estimated based on intake air temperature which is detected after the vehicle runs for a prescribed time. The idle stop of the engine is inhibited in response to a request from an air conditioner or to avoid cool-down of the engine to be restarted. In addition, the idle stop of the engine is allowed or inhibited in consideration of remaining battery charge, particularly in the case of a hybrid vehicle which is equipped with a motor/generator in addition to the engine. The engine is automatically restarted to avoid unwanted reduction of the remaining battery charge.