Interesting fix. If that doesn't work out, I've been using a Sunbeam 732-500 heating pad. Three levels of adjustment and no automatic shut off like the new ones. Heats my 15cf freezer just fine without over shooting. I just inherited the old house chest freezer to use for lagering, so I bought a couple new sunbeam pads on eBay. One for a spare (or third freezer someday) I think they were under $20 each.
Let us know how the hair dryer works out.