Need to know the color of the smoke. If it's blue, suspect oil is seeping past the valve guide seals after the engine is stopped. If there was any recent problem that could have resulted in excessive gas in the oil, that would dilute it and allow it to sneak past the piston rings. The oil should be changed right away when that occurs. Leftover gas will eventually vaporize and be drawn out and burned.
Black smoke is due to too much fuel.
White smoke is due to burning coolant due to a leaking cylinder head gasket. Most of the time that doesn't go away but it depends on where the leak is and how it is affected as the engine warms up and parts expand.
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Sunday, March 15th, 2015 AT 3:41 AM