PURPOSE: To optimize a fuel consumption, by rewriting a next target idling engine speed stored as a map according to an optimum cooling water temperature rising curve.

CONSTITUTION: A cooling water temperature rising curve such that a warming-up speed and a fuel consumption, etc. are optimized is preliminarily obtained, and it is stored in ROM 16 as a map including a time for parameter. After starting an engine and continuing an idling condition, a cooling water temperature T of the map with respect to an elapsed time after starting of water temperature rise is compared with an actual cooling water temperature T' detected by a water temperature sensor 5. If T<T', a map of a target idling engine speed is rewritten so that the target idling engine speed before a fixed time may be increased, while if T>T', the map is rewritten so that the target idling engine speed before the fixed time may be decreased. Then, the map of the target idling engine speed is stored in RAM 17. An idling engine speed control actuator 2 is controlled according to a deviation between the target idling engine speed and an actual engine speed.