I have a new Nano 16g mini with the little LCD screen. It is not one that came with a HD, but bought at Walmart.
I have played this thing on the battery for more than 40 hours without charging many times. I bought it specifically for the '09 SERG and my iPod Interface Module. I've not had to reset it yet, but it's nice to know the three button option is there if needed.
To address the durability and heat issues, I had mine clipped to my work shirt collar and forgot to remove it before throwing my shirt into the dirty clothes basket. My wife missed it and threw it in the washer. It went through a hot water cycle and then got thrown into the dryer for another very hot cycle. When she gave it to me it was still almost too hot to hold.
Amazingly it works just like before. I've yet to have an issue with it after the wash/dry cycles. It's a very robust piece.
I also have a very old Gen 3 click wheel 40g and it's battery is shot, but I use it in a dock with power without any issues.
Good luck with your warranty...