Time to get him out of house - but it's cold in coop, help?

I had two birds in the house being treated for goupy eyes. The hen was fine after one overnight. Put her back into coop. But Mr. roo has been in for 2 or 3 days, on a heating pad off and on. Both of his eyes were goopy, and I think he had Gape worm too. After one dose of wormer that part was better. But one eye has taken longer to clear up.

So today he looks good. But temps have dropped to 30's overnight and we had snow last night. I normally wouldn't worry but he's still be shivering some in the house and so he's continued to be on and off with the heating pad. Now, it's possible the sly little guy is just working me over to get to stay in but I do want to transition him back to the coop.

I know birds are much hardier to the cold than the heat of summer, but I'm worried about going from 60-some degrees inside to 30's outside. I don't want him sick again from the sharp change.

Any advice on how to proceed?