I've tried.... and ended up with a full WiFi smoker controller. Bluetooth range tends to be short, especially Bluetooth LE. That's done for longer battery life. Depending on your house construction, you may not even be able to make a connection to your transmitter.
What probe do you have? I ended up going with the Thermoworks Smoke because I know they have the add on connector to run it over wifi if I feel fancy in the future.