300E cold start question
 

I have an '87 300E automatic. I have noticed that this car idles at the same rpm from a cold start (e.g., after car has sat overnight) as when engine is fully warmed up. Is this normal, or should the idle speed be bumped up automatically when it is a cold start? I ask because the idle is a bit rough when the car is cold started, and gets a little rougher when first shifted into drive or reverse from a cold start (it smooths out after a couple minutes). Thanks