Inside the house is your best bet.
Anything is possible so yes it would be possible to heat the outdoor space but the cost would surely be prohibitive unless you are Bill Gates.
If you are talking about domesticated cage finches like Zebra, Star, Strawberry or Gouldian, there is no way they can handle those temps.
Native wild finches are fine with it but those are illegal to keep as pets.
To the best of my knowledge any of the former species I mentioned are from...