Thanks for all the info, Pinecone! If I ever have a spare lithium ion battery, I'm going to have to connect it to my car's battery via jumper cables and see what happens!
Actually, I know what you mean about overheating. I bought a Packard Bell portable that has a sticker on the bottom: "NOT a laptop." I guess it's that kind of battery that makes the difference between a "portable" and a "laptop."
I have just been talking about the battery for my Sony in this
other thread. It started about something else, but it led me to discover that the battery has an impressively long life. I'm on three days and counting, and the battery indicator has not gone down one notch (minimal charging - just enough to pass a few files).
I'm going mobile phone shopping tomorrow. Wish me luck finding one with the right power plug!