Not worth it for a new thermostat.
How is this the only post mentioning duct tape?!?!
It has a million uses. Attaching paper to vertical surfaces is one. Fixing a hole in a canoe. Building a new wallet. Helping babies crawl (don't ask).
Duct tape - plain old gray sticky tape with a mesh - is usually the first thing I turn to.
All great ideas are controversial, or have been at one time.