One of the differences between a warm and cold engine is idle speed. A higher idle speed will place more torque on the engine mounts when in gear, showing up a collapsed mount. If the shaking seems much worse in gear than in neutral, that is what I would suspect. If the shaking continues with a cold engine that has dropped to low idle, but not when fully warm, then the engine mounts are less likely than a fuel supply or ignition problem.

Steve

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'91 MB 190E 2.3
'08 RAV4 Ltd 3.5
'83 Lazy Daze m'home 5.7