Thought I'd give an update.
I let my phone go until the battery died. No actual use, but the usage indicator said I had used it for almost 20 hours. Standby time was a little over 24 hours. Ridiculous battery life AFAIC.
Charged the battery up all the way. Started using the phone and, lo and behold, the problem seemed to have fixed itself. Not mind boggling battery life, but an amount I could live with. I forget what I got, but it was about 8 hours use and two days standby.
I brought it in to the Apple store to have a counter tech (sorry, I have trouble with the Apple term "Genius")look at it. The tech was rather dismissive, saying that there was probably a third party app running in the background that was causing all the problems. I said that was rather hard to accept since I didn't open any third party apps at all since the restore I did. I tried to show him the series of screen captures I took which documented the lack of use and the rapidly disappearing battery life, but he had absolutely no interest in looking at it.
In the end, I was offered a new phone or I could return the one I had for a full refund (seems to be a new Apple theme). I accepted the new phone, even though I was on the last day of my 30 day trial, so if this one has problems I'm SOL as far as ditching the thing.
So far, the new phone seems OK. Not spectacular, not as good as my 3G, but within reason. Set it up as a new phone yesterday afternoon and got it fully charged. So far, 5 1/2 hours actual use, 28 hours standby and I still have 33% showing. Maybe a few more full charge cycles will bring it up to where it's supposed to be.
Here's an interesting thing I picked up from several conversations with Apple so far. Sometimes an app can start to run in the background (even a native app like Safari)and can't be seen even in the multi-tasking bar. Don't know why, but everyone I spoke to agrees that can happen. A soft reset will shut the phone down and any apps that may be running. It was recommended to do this once daily as general maintenance and good housekeeping. This will also happen when you let the battery go all the way until the phone shuts down by itself. I suspect that there was an app running in the background and when I let the phone run down, the app was forced closed. This seemed very possible to the techs at the Apple store. It doesn't explain the overheating, but that hasn't happened again, either on the old phone or on the new one (so far). Interestingly, the new phone came with OS4.0 installed instead of 4.0.1. I'm leaving it that way for the time being, just in case the update caused the problem in the first place. I can live with the old style signal bars.
I'm done on this thread unless I have an overheating issue again. I will, however, be monitoring the low battery life issue, an I'm far from the only one who's been reporting this problem.