I had a similar sound on my 83 300cd and it was the center driveshaft support which had completely disintegrated and was allowing the driveshaft to flex when accelerating....The only difference was my car did it all the time and not related to temperature or other things...If that is whats wrong its too bad it didn't get it replaced at the time you had this other work done as it is easier to do at that time. I am also suprised the mechanic didn't notice it was bad. As a test you can get under the car and push up on the center of the driveshaft and if it moves up and down that support is bad.....

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83 300CDTurbo 307,000
2005 Honda Element 266,000
56 Nash Ambassador Country Club Special 34,000(under restoration presently)

http://www.peachparts.com/shopforum/car-audio-multimedia/125099-123-install-extreme-dynamat.html