My DVR gets pretty hot. Careful boxing it in.
Mine is behind the tempered glass door of the equipment rack, so it's not much of a bother, but I think the noise is from the fan. Might wanna check yours to see if there's a nasty build up of dust on the blades. Also, see if there's much play in the fans shaft. I really doubt the sat companies put much in the way of quality fans in there. You could probably replace it with a much better (quieter) unit for pretty cheap.
The rubber feet idea would help keep the vibrations from transmitting to the rest of the equipment around it as well.
When it's at it's worst, you could poke and prod around the outside of the case to see if it's part of the chassis making the noise. Then you could tighten the screws or place a weight on it.
If you're really feeling adventurous, you could line the internals with the sheets of that black stuff....the name of which escapes me right now. "Black hole" I think they call it"??

Bob