I've had a thermal fuse go in a small transformer that looked like new. But, it had been in service for 15 years. I replaced it with an external fuse. The key issue is to inspect the transformer for signs of heating, like deformed plastic wrapping, scorched areas, etc. If there are no signs of overheating, odds are the thermal fuse went due to "age stress" or a brief power spike that caused more than 2A to flow though it (enough to blow the fuse portion).
These thermal fuses can fail at times. In my case, the replacement external fuse is fine, and equipment has been running with no issues after 2 years. Of course, one could replace the original in the same location (in transformer) and re-tape it back in place...