Have never done this, but it should be doable, depending on the design of the remote temperature unit.
If it uses a discrete component for measuring the temperature (like a LM35 temp. sensor), it should be easy enough to remove it from the circuit board and mount it into the stator, with extension wires.
However it's hard to tell whether it's actually possible with the particular temp. unit you have. Got to see what's inside.
So the answer is yes, it's doable in theory, but exactly how depends
Do you have a temp. sensor that you intend to use? If so, open it up and post a good detailed picture of the parts of the PCB. Then we could start giving more to-the-point advice.
And I agree on the thinking bit. Can be scary, no, downright frightening.