To be 100% certain the fan is off... disconnect one of the two wires. Some members actually calculated how much
12v battery is used, as well, when the fan runs.
I did a Thread about my experiences in our 2014 25 foot International. The 'thermo switch' as well as other terminology seem to the problem. Some times I could unplug and replug and the fan shut off. There are temperatures ranges where the fan 'thermo switch / aka snap switch' is activated.
They shut down once below that temperature. That was the general idea... some members have some sophisticated systems. Good luck. Well discussed on the Forum.
The fan can become very noisy as well. There are better and quieter ones that other Airstream owner have tried. Available on the Internet and prices vary considerably for the identical snap switches and fans.