Sounds like your following the caresheets to a "T", which could give you a very dead kingsnake. Kings in the wild, despite what the caresheets tell you, do take advantage of basking temps much higher than 82. I have personally seen Eastern kings basking in areas where the substrate temprature was as high as 100. Many people force their snakes to live in a very narrow temprature range, which might work most of the time, but your not supplying what the animal needs. The broader the range of temps you can give the animal, the healthier it will be. I have kings that eat small to medium rats and will then sit right on top of the heat tape, which is 95-100 degrees, for short periods of time. Then they will move to the middle of their sweater box, which is in the low to mid 80's, until the meal is digested, which usually only takes 3-4 days. They have a much healtheir appettite, and grow much quicker than kings kept in a narrow temp range. The key is to give them as wide of a gradient as possible, 100-70, which requires a larger cage. I know most people can't supply such a broad range, but I would try and atleast give them 90-75. I would also do a search through the forum for Frank Retes, FR, posts on this same subject. He's much more eloquent about the subject than I am.
Like I said, a healthy king may do okay at 82, but if it does become exposed to protozoans or a respitory illness, then it will need higher basking temps to overcome these illnesses. Higher temps help jumpstart a snakes immune system, and metabolism. Good luck!
-Phil