Rough idle on restart

[NEAL560SL]

I have a 1986 560SL and am hoping someone can give me an idea if there is a typical adjustment or part that could be causing my problem. Cold start the car starts and idles perfectly, however when restarting when warm it will miss or chug like it is probably too rich. If you step on the accelerator slightly it clears up in a matter of seconds. I haven't actually had anyone to start it for me so I could see if it is smoking black from the exhaust, but I expect it is. When I say it does this for seconds, it is literally 5 to 10 seconds or less.