Sound like you may have an Air Leak.

What I had to do to get rid of the my when Engine hot vibration/shaking:

Raise the Idle speed within the normal range (this helped some; it was around 700rpm). I raised it to about 750 rpms.

I bought a new Rack Damper Bolt but it did not help much. I have a turbocharged 300D Tubo and it has a Rack Damper Bolt.

Rebuilt my Injectors with new Nozzles (This took away most of the shaking)

Doing a Valve Adjustment (took away some more shaking). If you can adjust the Valves yourself do that first except for the new Valve Cover gasket is free.

Changed Motor and Transmission mounts (took away some more vibration)

Found that I had a small air leak that showed up when the Engine was hot due to hard fuel inlet lines that did not seal even with the clamps tight.

Finally was able to use the Rack Damper Bolt to tune out a little more shake. (that bolt was made to reduce the shake on a new engine; not to compensate for a bunch of worn and out of spec parts

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84 300D, 82 Volvo 244Gl Diesel