It's really unfortunate that you have had two bad Nooks. I wouldn't say that all are lemons though. I had a Nook Color for a year before I bought a Tablet to replace it. My sister has my Color now. I haven't had issues with either.
I will say that the adaptors and charging cords need to be made better. However, that isn't the Nook devices. FYI- did they replace your power adapter too when they replaced your cord? It sounds like that needs to be replaced. Getting over heated isn't the Nook or the USB cord; it's the adapter.
As for your battery a couple of things might be happening.
1) You have a bad Nook. Get it replaced. (I know this is unfortunate, but better for you to have something that works, than doesn't).
2) One of your apps is running and draining your battery. Here's a question, do you have your email app set up? If so, what refresher setting do you have it on? If it is refreshing your email every few minutes or so, that can be draining the battery. Test your Nook by turning off the wi-fi over night.
What apps do you have installed? Maybe I can figure out if you have one that is draining the battery.
I'm sorry you are having so much trouble.
Also, do you have the latest software on your new nook? (1.4.2)
Not having that can cause issues.