I have heard about the motor mount inserts, I have heard they help transfer vibrations. I've got enough vibrations and rattles already. (currently working on sound deadening the whole car)
I suppose I'll try to check to see if the motor mounts are decaying. If I need to replace them, I'm probably going to go with new rubber ones. I'm being realistic about my car. It's what I drive to work, It isn't going to be fast any time soon, so I'd like it to at least be comfortable.
By the way, this still doesn't explain why the problem stops after a few minutes.