My house gets down into the mid to low 60's at night during the winter, and my snakes are fine with just their UTHs. Be careful not to fry your snake- that's a very powerful bulb.
See your hollow log hide? The plastic one? I had a very bad experience with that hide.
http://tinyurl.com/4vur9w
You might want to seal off the hollow end or even better saw it off to prevent misplacing your snake. See the bad thing about him being up in there is you can't _prove_ he's in there, so you're worried he may have escaped. You can't see the secret passage, but you may be able to feel it. I have a few of those hides, all altered so there is no blind limb, and the snakes still love them.
The half log. The baby will most likely be afraid to hide in it. Snakes like hides that are snug and cozy. I would recommend either using aspen as a substrate or scrunching up a paper towel and putting it inside the half log.
Reptile carpet. It works just fine, but it's a PITA. You need two pieces so you can remove one to launder it and have another to replace it. That's fine. But your snake will burrow under it and you have to remove everything to get him out. Eventually you will get tired of this.
Might I suggest aspen as a substrate. Babies (and adults) love being able to burrow. it is not natural for a wild cornsnake to just laze about out in the open. They are afraid of being eaten by everything. They appreciate a nice deep layer of fluffy aspen to burrow in. You would appreciate it too, compared to dealing with reptile carpet. I know, I have used both.
And you could add a paper towel roll for an extra hide. Babies (and adults) love those. I resisted them for a long time because they were so unnatural, but after trying a couple, now all my snakes have one.
Do you know that you will most likely need a thermostat or rheostat for your UTH? A UTH will get to 120F or higher and can burn your snake.
