What do I do with this thermometer sensor?

[xdeus]

I can plug the UTH into the outlet attached to the Ranco right?

Yep... that's what it's for.

does that mean I would put the t-stat probe under the cage?
because my UTH is on the bottom of the cage

It depends on how your cage is setup. If you can leave a little room for the UTH to stick out from under the tank, you can tape it directly to the UTH. The idea is to find a place for the thermostat probe that is very stable. If you place it in the cage, it can get moved around and will likely alter the temps. If you can't place it outside of the cage, try to find a secure spot in the cage such as under the substrate. Just don't tape it to the inside of the cage because snakes and tape don't get along too well.