The temp probe does not consume any power. What you wire the probe with depends on what type of probe you are using.
If you are using a thermocouple, it should have come with a coil of wire attached & that wire needs to run back to your controller. You can splice in an extension but the splice has to be at the same temperature as your controller or you will introduce an error. Splice in another wire up close to the pot and you will be introducing some serious measurement error & may not get a measurement at all.
If it's a thermistor you could use anything providing the wire does not add any resistance to the circuit.
If it's a RTD then you can splice but make sure that all of your connections are solid. The third lag of the RTD is a loop back from one side of the RTD & is used to average out the wire resistance. And adding any resistance difference between leads will affect accuracy.
I had this same question recently and did some research and came up empty. I wanted to be safe so I ended up ordering the same exact cord extension from Auber for my RTDs. My question is what's the best way to splice them together to keep them accurate? Solder? Wire nut? Terminal block?
The only benefit of using RTD wiring over say doorbell wiring is the wire color standard. You can just as easily extend your RTDs using doorbell or Phone wiring as long as you use the same gauge or replace the wire all the way to the connector. Mixing wire sizes can cause issues. Heck, you can even use 24 ga CAT-6.