Wireless, Bluetooth, High-Temperature Thermometer

But in the case of bluetooth, I was hoping it could connect to a phone directly and an app on the phone would be able to read and display. Is this not possible with a low-power configuration? Ideally I'd want the battery (2 AAs for example) to last for at least a couple months.

The TI Sensortag is a Bluetooth Low Energy tag powered by a coin cell battery with temp, humidity, accelerometer, gyro, etc. sensors. Free IOS and Android apps are available to read from the tag. The tag is a demo project for a TI BLE chip so I am not sure how reliable it is. I have no idea how long it will last in a 200 degree sauna.