My daughter uses an iPod Nano that I received as a gift from SolidWorks a number of years ago. It suffered from the battery overheating problem, and my daughter was loaned an unused iPod Mini (in bright green!) from a friend. In the meantime, I learned of Apple's replacement program to handle out-of-warranty battery-damaged units, and got my daughter's Nano replaced at no-charge. Which she still uses to this day.
In the meantime, she added the bright green Mini to my mini museum of old cameras and computer hardware, for the Mini's battery barely held a charge.
After I discovered the replacement touch screens for the Palm TX, I looked around eBay for replacement batteries and was stunned to learn they were just $5 (or so), complete with tools and printed instructions. I ordered the battery with the largest capacity I could find.
While I waited for it to arrive, I found a video online that described how to take apart the iPod Mini, which looks like it was made with new screws. Basically, you attempt to insert a small flatbladed screwdriver between the metal case and the white plastic end caps, pop off the endcaps, and then remove a few more items -- metal spring clip, electrical connector -- and then slide out the guts of the unit.
I was surprised to see the many capacitors on the mother and daughterboards. The large number of components overwhelmed the sparse number on the Palm TX's motherboard.
The battery arrived, I swapped them out, and reassembled the Mini. It works again.
My daughter and I are wondering what to do with it and its 4GB capacity. One idea I have is to bump up the capacity using a replacement 30GB hard drive (about $50 on eBay) or 32GB CompactFlash memory card.