I don't think you should attempt to repair the thermometer. Most older ones have mercury and should be disposed of properly anyway. Besides think about where you found it!
Wait, you mean the floor? On a trailer of your vintage and size, the floor at the back is very important to prevent rear end sag. If you have a large section that is rotted or gone you may have to replace a whole section in the rear. It would be a good idea to inspect the frame at this time also. I would suggest searching on rear end sag and to proceed from there.
Wally Byam Airstream Club 7513