It's a Florida King. And yes you dont need the temp to go any higher then 85. Kings like it on the cooler side. You'll probably even find him spending more time on the cold side then the warm side of the tank. And if you wanted him to be on the big side a Kindsnake is the wrong choice. They are smaller snakes. He is most likely full grown by now. They usually max out around 4 years but if he is already the size you say he is(and he looks like it by the picture) he is most likely as big as he'll get. Some care sheet say they will get to 5or 6 feet but they usually are around 3-4, so really you already have a "big" kingsnake by standards.
A care sheet saying a kingsnake grows to between 3-6 feet would be the equivalent as saying humans get to be between 5-8 feet. There are some humans that do get over 8 feet but that deffinatly isnt the norm and doesnt happen often.