This definitely looks like a fuse. Is this wire powering the heating element (would be at mains voltage) or is it a low voltage line? That would tell you if it's a fuse or a sensor.
If not a fuse, then it could be one huge glass NTC thermistor used for ambient temperature that factors into PID regulation. That would definitely throw an error if that were to fail. But then again, it doesn't look the part (not that I know all that much about glass thermistors). You'd need to know its value or calibration would be way off.