Guys, I think you're missing the most likely culprit.
Given that it's smooth when started cold and only shakes
once warmed up, it's likely the rack damper bolt on the
injection pump. A bad injection pump or bad motor mounts
would shake all the time, regardless of engine temperature.
The rack damper is located on the backside of the IP,
just below the shutoff valve. To adjust it, loosen the
locknut, then turn the main bolt inward. There's no
formal adjustment procedure - just turn it in until
the idle is sufficiently smooth. Too far, and the car
will tend to stall. You can't hurt anything by adjusting
the rack damper, so have at it.
The good news is this task requires all of 10 minutes.
The rack damper does occasionally go bad. If so, you
won't be able to tune out the idle vibration. Your dealer
can supply a new, upgraded rack damper. Price is about
My old '84 300D shook like crazy at traffic lights until
I learned this trick. One adjustment and it was smooth
as could be.