I’m not sure how well silicon would work, I would give epoxy a shot. Here’s one of my favorite hack How to make a Sawed-off USB Key | Evil Mad Scientist Laboratories
Also, it seems dipping a drive in epoxy has already been done:
One person is reporting overheating. I would try looking into electronic potting epoxies, they might have better heat transfer properties. Also, try to keep the amount of epoxy as thin as possible.