The answer to your question is NO! A grey is a special bird that requires being nurtured by it's flock/you and any family members you may have. To isolate him alone in a room is ridiculous, especially at night! Never mind the cold!! They are from AFRICA and can not take the cold. Even a draft can make them sick. Never mind fluctuating temperatures!!
Everyone here is being way too nice, because I know that no one here would even think about putting their grey where you want to. Tari is right, there will be chilly days where it will be easier to say, Oh, He won't mind. I'll see him tomorrow. What you will end up with, should you NOT take our advice, will be a VERY depressed bird, one who will develop behavior problems that probably will last a lifetime, a feather plucker, and a trauma he will experience, that he MAY get over, but never forget. If you can't love that grey like a member of the family, then you should GIVE him to a family that will. I'm sorry if this sounds like I am coming down on you, but I am!
This grey deserves better than being left in a shop because it's cage is too big!