I have a setup pretty similar to yours... at this time a carpet isn't in it, but I do have 2 corn snakes (big ones) living in it.
Personally, I use a cobra heat mat under the bottom and a spotlight at the top of the cage (thats protected by chicken wire). I think that just the chicken wire could work, but the coffee can lets me run the light and sleep in the same room.
With the chicken wire (depending on size you may have to double up on it) wrap it in a circle and fasten in to the top, then get a small piece and flatten it out, and use twist ties (or something) to fasten it to the other chicken wire on the bottom.
If you don't understand I may be able to post some pictures later.
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Currently have: Antherystic Corn Snake, Amelanistic Corn Snake, Oakatee Corn Snake, Leucistic Texas Ratsnake, and an Eastern Fox Snake
Saving for:
Jungle Carpet Python, Frilled Dragon