Hi again Malaina,
As others have said, 50 degrees F for longer than a night or two is asking for trouble. They can tolerate it for short periods of time, but you run a much larger risk of your Beardie developing an upper respiratory infection. Most sources say that you run a risk of one whenever the nighttime temperature drops below the mid 60s.
When it comes to strategies to avoid temperatures this low in the case of power outages, you have a few options.
Hot water bottles may work, though to last a full 9 hours they would have to be quite large. You would also have to ensure that the surface temperature was cool enough that your beardie wouldn't be at risk of burning itself.
Chemically based heat packs are also an option, and perhaps the easiest solution. However, you want to make sure you are buying the right brand, and again, making sure your beardie has no chance to burn itself. There is a company called Ship Your Reptiles that sells awesome, long duration Uniheat brand heat packs that would probably be your best bet.
Honestly, though, how are you coming up with 40 degrees F inside your home (presumable where the bearded dragon is) from only a few hours without heating? I live in Michigan, and even when we have a power outage in the middle of winter, the interiors of my apartment, my grandmother's house, and my parent's home all remain reptile-friendly overnight without heating (assuming that they were heated during the day time). In fact, I usually turn my heating/cooling off every night at 10PM and turn it back on again 7:30AM as my daily ritual to save on my gas/electric bill, even during the winter and have never had it get colder than ~67 degrees F. According to what weather maps I've seen, your winters should be a lot warmer than mine, so it doesn't make much sense to me that it would be a problem.
My honest advice is to get a box of maybe 5-10 uniheat heat packs in case of emergency, but also get a thermometer display that records both the lowest and highest temperature it experiences over 24 hours. The first time your heat goes out during the winter, provide the emergency heating measure, but more importantly set up that thermometer near your reptile tank to see how cold/hot it actually gets. Heck, get a few and set them in each room to see which one stays the warmest at night! You might be better off providing no additional heat and instead just making a temporary habitat in the room of your house that stays the warmest overnight without heating (if it's not the room you keep your reptile(s) in already. It is for me, but then again my reptile room is always 5 degrees hotter than the rest of my apartment).
Hope that helps!
-Ellen