Remote Fridge Temp Sensor Wiring

I just bought a “Camco Fridge Alarm”. It has a sensor that goes in the fridge and a digital readout panel that tells the temperature in the fridge as well as the room temperature. It also has an alarm feature. The sensor and readout unit are connected by about 2 feet of light 2-conductor wire. I would like to modify it to allow me to read the temperature when the TM is open or closed.

My plan is to either install jacks of some kind in the wire from the sensor so that I could plug the readout panel into one inside the TM when the TM is open and have a second jack on the outside of the TM where I could plug the readout panel in and check the temperature in the fridge while the TM is folded down.

Or, another option I considered is to just splice in a longer wire so I can dangle the readout panel out between the lower wall of TM and the upper shell when it is folded. I am concerned about how I would secure and protect the readout panel from the elements though.

Ether way, this is going to extend the length of wire between the sensor and the readout significantly.

Questions:

1) Has anyone done something like this already?
2) Does anyone know enough about how these things work to know if I change the resistance in the wire by making it longer if the temperature will still read accurately?
3) If so, can I work around it by increasing the wire size? Could I calculate or measure the resistance in the existing wire and try to match it with a longer but heavier wire?
4) Could anyone suggest a good type of connector jack to use?

I will appreciate all comments and suggestions. Thanks!

Jim