Leave it be, those are designed to go directly on the glass. Awesome you have a thermostat! : ) Removing it can bend the wiring inside the pad. To relieve your concern, try placing a piece of indoor / outdoor carpet over the hot spot and then putting other substrate on top. That will provide an extra barrier.

What she ^ said.

Don't remove it.  Like Sonja said, it's bad for the internal wiring.

If you're worried about your little corn snake burning herself, invest in a temperature gun!  Even with a reliable thermostat, a good temperature gun will let you know for sure what the temperature is where your baby is laying.

I thought about the carpet thing, but people told me it quickly gets full of bacteria, so I'm not sure if I should use it...

I used to use it, and I had 2 pieces. When one was soiled, I removed it and replaced with the other. I took the soiled one and soaked it in a diluted bleach solution to disinfect it, then rinsed it thoroughly and air-dried it so it was ready to use for the next time.

And go Em! Yes, a temp. gun is one of the best investments a keeper can make!

I never used a barrier when I had my corn on a uth. If the thermostat works good I don't think youd have a problem anyway depending on what the temp is set at.

Also, depending on what your ambient temps are, you'd be surprised how little a corn will use hot spot anyway.

Do you have the little silicone nubbies that come with the heater applied to the corners of the tank to create a gap for air flow?

yes, i use them, also to not crush the wire :)

I dont want to get attacked but I'm a carpet man. I hate trying to clean an enclosure I cant lift full of chips. I like how easy contractor paper is to replace but hate the look & know my snakes dont enjoy not having the traction. Just make sure you give it a good look over or light spray like you do chips prior to use. I use the grey indoor/outdoor carpet they sell pre-cut at lowes for $20. I believe the size is 6'x9' & I actually use a template I made that is exactly half the size of the floor of my enclosures. This way if I can replace just half of the rug if one side is fresh & clean. My 3 enclosures are 48"x30" so I'm sure you'll get a lot more out of a roll then me but for $20 buck you cant beat it.

I don't think there is anything wrong with using carpet as long as you stay on top of the cleaning. And I know you do.

I won't bash you forthe carpet - I still use it in my tortoise enclosures - they are converted PVC cages. I put the carpet on the bottom to give them traction and then timothy hay on top. My Baron's Racers that are in a converted front opening aquarium also have it for traction. : )

carpet is indeed good for traction......

You can also add a slide dimmer cord inline with the T stat  so it works like a poor mans proportional Tstat

Would a silicon pad work well as carpet? I figure it would be easier to clean, maybe less porous than fiber...

No. Silicone will trap the heat. It won't diffuse through it like carpet would. I still dont think you need anything. Just put a nice layer of aspen down, set your heat to about 85 and call it a day.

I think I will let the pad as it is, with thermostat regulating the temperature. I just hope the thermostat won't fail.
To secure the thermostat sensor to the glass, so the snake doesn't move it, I'm thinking about using silicone glue (glue-gun). Is this a good idea? I'll glue the wire, not the sensor itself.

I secure mine with foil tape.

What are you using to measure the temps. right now?

As mentioned previously, if you don't already have one, I'd recommend getting yourself a temp. gun. That way you can keep a watchful eye on the temps. and that is great for peace of mind, too. 

Wait is the heat pad on the inside or the outside (underneath) the tank?

With proper substrate in there like the carpet, or any bedding really she should be okay. You can also secure your thermometer with a peice of electrical tape so she can't move it. With a temperature variant in your tank your snake will be able to decide for her self if its too hot and move to where it's cooler. My UTHs never want to stick I'm surprised yours is still clinging on. Temp guns are great as previously mentioned.

it's on the outside, under the tank. To mesure the temperature, I use this: http://www.lacrossetechnology.com/9245/index.php It has two sensors. How much and where may I get a temp gun?

Amazon

You could also use a square of flooring tile to diffuse the heat. Most home stores might even give you a piece for free if you ask. While your there, you can pick up a temp gun. Both Lowes and HD carry them near the welding stuff. Some pet stores carry them as well. You can get them from all over, and it is the best husbandry investment you can make. I use mine daily. (a rayovak from HD $25 and a PE mini I use in the feild and to back up the other one.. just in case..)

Ok, well I left the UTH as it was and used silicon glue to secure the thermostat gauge. Warm spot indicate 27-28 Celsius.
Checkmate is now in his new vivarium and sniffing around! Thank you! I'll try to buy a temp gun soon :)