When you say, "install a real fireplace", do you mean a natural gas or propane unit? In those cases, the combustion chamber is sealed and vented outside, so the combusion gasses pose no risk -- and modern units have safe-touch glass so there's no burn risk. This option is fine.
It's extremely unlikely you're talking about a wood-burning fireplace with chimney (unless you already have that, because otherwise that's a huge renovation) -- risk is smoke and burn injuries.
You could also be talking about a wood-burning stove, which could be realistically retrofit -- these units gave risks around smoke escaping into the indoor space, and burn injuries.
Lastly, I'm on a mission to crush the notion that candles are a legitimate emergency heat source (they're not, their BTU output is way too low). On top of that, they're a fire hazard from tipping over, and unsafe for use around birds. Just stop. Everyone.
So, what to use? I think your birds are in a single small-ish cage (if I'm remembering correctly). I'd suggest a hot water bottle filled with hot water from your standard water heater (which is insulated and will stay hot for a long time after the power goes out). Place it in the base of their cage. Also, a small inside room will retain heat for longer than a large exterior room with windows, so you could temporarily relocate them to a walk-in closet for the duration of the outage.
How long are the outages you're expecting. Suitable responses will vary depending on that detail.
I suppose the last thing is to remember that normal healthy birds aren't going to drop dead if the temps drop into a range that isn't exactly comfortable (uncomfortable for you doesn't equal unsafe for them... or you).
