Did they confirm your battery issue? It is well known that it takes longer to charge because of the new larger battery. People were discussing this issue on Friday. I dock mine at night and run the clock app (as I mentioned) and it is always charged in the morning. I did the same thing for years with the original, so it isn't an issue at all for me. Also, like I mentioned, I streamed video on it while it was plugged in and the iPad stayed at 100 percent battery power. I still think you have a bad charger, a bad outlet, or a bad iPad.
The heat issue could be a problem for people using their iPad without a case. I have not noticed the heat at all when I had it in a cheap pleather case, but after I read an article on the subject, I pulled it out of the case and it was warm. Not nearly as warm as most laptops, but it is a lot warmer than the always cool original iPad I own.
As the article mentioned, the original iPad would shut down when it was hot outside. Obviously, the new iPad is already running warm, so I don't think the shut off default is set as low. I am curious to see how it holds up to outside heat when compared to the original.
* Also found it interesting that the one article used the number of hits on a forum in the article. These hits do not mean that people are having the issue and the number of responses don't either. Many people read these type of threads when they first buy an item or are considering buying an item. Also, some people just like to see if they can help solve an issue. Like I mentioned above, I never noticed that it was running warm until I read an article about it. The fact that I clicked on the article does not mean I was already having the issue.