Would a temp controller help in a situation like this, though? This is one of my biggest fears, honestly. As Aquavaj (lol) mentioned, with the probe out of the water, it would read a much lower temp, and continue heating the water.
Correct, the air temp would be giving the controller a false reading and thus continue to send power to the heater.
lesson here for those reading: Sensors do get knocked out of their tanks. Set the heater for an upper limit in an acceptable range and on the max/always on leaving only the controller to turn it off in the case of a malfunction. Secure your probes/sensors or least secure the cords so they keep the probes/sensors in the water in case they get bumped. There are acrylic probe holders. Sometimes I use small plastic clamps fromn the check out impulse buying display at the big box hardware store . If a sensor/probe does get knocked out of the tank, not only will the heater not turn off (unless tripped by it's own thermostat) but you will not get an alarm.
Sorry to the OP and hoping for the BTA to recover.