It's honestly a toss-up: If your corn moves to the 71* area, he needs part (not more than 20% & possibly less) of his home heated to 85* by UTH (-preferably). If he stays where he is at "up to 80*" you can leave his heat OFF, except maybe offer it after meals & see if he uses it, or if this is an adult corn snake (that uses branches) you might try an overhead light (dimmed!) for a few hours of basking time per day, as needed for digestion. Either way, watch what he's doing: if he's too warm, he'll be in or around his water bowl much of the time...so take a hint about what's most comfortable for him by what he shows you. Of course, "up to 80*" might mean 77*, so he still might need a bit more heat to digest. Compared to my house in summer, it's not below 80* for at least a month or more...but I wouldn't expect that to be optimal for ALL year, does that make sense?
Corns are pretty flexible...my home is set to 70* (heat) in winter, & in the summer, my A/C is set to 80-82*...at that time most of my snakes' heat is OFF, for maybe a month or so. (with some exceptions- but certainly for my corn snakes) And btw, I've never had a corn snake with an R.I.
That's a good question & not off-topic at all. Living with snakes is just about making it work for you & yours. Between the 2 options, if your temperatures are
as described all year, I'd move him out of the snake room, to where he has more temperature choices.