Agile,a thermostat could fail in a year,so your mileage is not relevant.
If you think the 'stat is failed wide open(heater cold,temp gauge down etc)Then you need to get it fixed asap.so the engine will run warm and efficient.
You don't say what the symptoms are with the rad fan.I would doubt you will get hot enough to trip it with a open 'stat.If it is running none stop then there could be a faulty thermo switch on the rad or a shorted wire.
Normally,you can test the fan motor by disconnecting the wires from the thermoswitch,join them together and with ign. on the fan shoud run.
If that is ok,you need to stop with the engine idling after a run,as the heat soak takes place,the temp gauge goes up close to the red and the fan cuts in until the temp is normal again.