Well, the customer service was fine... my story went like this.
I went in, it was 7:33, my appointment once I signed up for the genius-bar was 7:40.
It was 8:10 before they were ready for me - whatever, I understand things like that can get backed up.
I tell the guy what happened... that it was working fine, then it shut off, and when I picked it up it was scalding hot, and that it wouldn't turn on unless it was plugged into the computer, and the minute you did that, it heated right back up, very quickly, regardless of which computer I plugged it into.
He then told me, that he was pretty sure that it was because I hadn't updated the software on it since I loaded it up in February or March.
Smelling a line that they'd tell to some computer-illiterate dolt, I increduously asked him if he was really telling me that my iPod could light itself on fire because I hadn't updated the software, despite it working fine for the last 6 months.
He said, oh yeah, the software regulates the power and the machine might not know what to do with the extra charge from the USB cable and blah blah.
I was confident that he was completely full of ****, but I said okee-dokee.
He took it in the back to do a software-restart (that's what he called it...) saying that he's seen this before and updated software and a reboot would fix it...
Then, predictably, 10 minutes later he came out with a new one telling me that it got too hot too fast to even work with to try his methods and that he was just going to give me a new one.
So, end of story is that they replaced it after a few minutes of B.S'ing with no questions asked. It's a refurbished one, but it looks like new, and works fine. The guy insisted that the refurbs are new cases, new hard-drives, and new motors and that the only thing that's ever possibly not new about them is 'sometimes' the LCD's are refurbished. Given his B.S. before, I don't know if I believe him - but either way, it's the best they were willing to offer me and I didn't have much of a choice otherwise.
I'll probably be going back to pay the $59.99 to extend the warranty for another year given how easily this crap happened (after all the horror stories from my friends too about their broken iPods...).