W126 Stumble at idle
 

Good day, I have a rather odd problem with a 1990 560SEL.
Cold starts, and will run perfectly all the way up to operating temperature without any problems.
Once the engine is warm, if I shut it off, and restart it while warm (say after stopping at a store) I will then have an intermittent stumble at idle. The engine runs fine while driving along at any speed, but at idle, it will falter every 20-30 seconds for the briefest of times. It will nearly die, then just as suddenly go back to smooth idle. Idle for a few seconds, then stumble again.
To reiterate, this condition only appears on a warm engine restart; first thing in the morning, the car will run perfectly for however long it's on, this only happens on a warm restart.
I am at a loss as to what might be causing this condition. I am looking for some troubleshooting steps that I can take to track down this problem.
Any assistance will be much appreciated.
Thank you,
Antony

Leaking vac lines, bad idle control valve would be good things to check first. Could also be the air flap/idle closed loop switch, if those malfunction the idle will be unstable.

Sounds like what it is doing is switching from mechanical-run (very low idle) to computer controlled.