I highly recommend using regulated UTH ("belly heat" works well for snakes, as long as it's not too hot, as they can/do get burned accidentally); using a light for warmth on a temporary basis is ok, but it needs a lamp dimmer from any hardware store, not expensive & very useful. I use some overhead lights (red & black bulbs usually) for warmth for some of my snakes that enjoy basking in their branches and you'd be surprised how fast even a low wattage bulb can over-heat a cage. That's probably why this snake had a bad shed too, heat lights really dry out the air. Corn snakes appreciate & do well with a humid hide* on the cool side of their cage anyway, with some damp sphagnum moss inside.
*Get a plastic food container of adequate size & shape, cut a hole (doorway) in the lid, put in soaked moss, & you'll find your corn snake in there quite often, really loving it, both for the humidity & the "cave-like" coziness.
And btw, that tank size is fine for now, but as corn snakes grow, I like a 40 gal. "breeder" tank for them ultimately.