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It's actually the module's temperature. The simplest way to retrieve it is with the gsmctl -c command. Or by using methods described in the other answer.
Yes, you can read and monitor mos of the parameters of the Router via modbus TCP protocol. In the following link you will find an introductory example on how to use it.
And also you can monitor some parameters via MQTT protocol. In the following link you will find some useful examples
Keep in mind that while Modbus is a little more complex is more flexible when you implement the whole protocol available. Is up to you the degree of complexity you need to satisfice your monitoring needs.