If the thermostat goes out will it prevent the cooling fan from working

What is your question?

It's been overheating a little and I'll turn the heat on to bring the temp down. 2 times now when I restart after it's been running I'll get a warning that the engine is overheated and should not be started. So I vent the reservoir and it fixes that issue. I've also had a warning that the transmission needs service now. Prob due to the thermostat. Now I notice the fan is not engageing