I would ditch the bulbs completely and get a small Undertank heater, bit enough to cover about one third of the tank. A Rheostat to better control temperature would be good too.
Corn snakes need a good temperature gradient...ambient temps should be between 75-85F with a hot spot (over the undertank heater) reaching to the low to mid 90'sF. This provides a hot spot for your snake to warm up. Make sure the other end of the cage is cooler, so he can thermo-regulate as needed.
Provide a hide in both the warm and cool ends...for such a young snake this can simply be a papertowel roll lain lengthwise against the wall of the tank, so one end is in the warm area and the other in the cool end. Two small plastic or clay flowerpot bases also work great. A hole will have to be cut or broken into them to ensure easy access. Hides are best if they are just big enough for your snake to comfortably coil in while still in contact with most of the sides. As snakes get bigger, the size of the hides will need to be increased as well. Best to go with cheap and disposable hides while your snake is a baby, then when they are full grown...(about 2-4 years) a more permanent hide can be bought/made. (I use papertowel tubes for my babies..or just folded paper towel for hatchlings...far cheaper and considering how fast babies will grow with a regular feeding regiment (I feed once every 5-7 days for the first year, then every 7-10 days till adult, which I then go to once every 10-14 days. Each feeding is an appropriate sized mouse or rat, about one to one and a half times the girth of the snake's thickest part of the body)
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PHLdyPayne