If you decide to go with a glass thermometer, I would suggest super gluing it to the side of the tank somehow. Super glue is safe, as long at the frog doesn't touch it while it is wet. The reason I say glue it, is to keep it vertical. If it were to tip and the frog gets on it, it could break. Better be safe than sorry.
Education is the most powerful weapon we can use to change the world ~ Nelson Mandela