In my experience, it is best to ground the tube damper if it is made of metal. Also, I would think that the damper should be in good contact with the tube. In such cases, it might be able to act as a heat sink for the tube. Unfortunately, there are other cases in which it will hold the heat of the tube in, and that could be a tube killer in time. Then of course, there are tubes such as the 3S4 in the Quickie that seem to produce no heat at all. That wouldn't hurt the tube if you were to get all crazy about damping it with such things as silicone, etc.