[Nexus One Accessories] d0ugie:
Charging the battery and using the battery both create heat. That said, the total heat you'd get from charging during casual use of the battery should not be great enough to warrant the nuisance of not being able to keep your phone on until you finish charging it each time. But 106F (41 Celsius) is indeed whopping hot and, according to not necessarily precise software tests I did on other HTC devices, that is the neighborhood of heat at which the phone eases back the charging current to the point where the phone may either charge at a current about even with what your phone is burning, leaving it without any net gain while running at too hot a temperature for the health of your battery or it will begin to drop the charging current toward zero so that your phone is discharging, waiting until the temperature simmers down until it turns the juice back up.

But what the hell is causing this if you didn't have things like wifi and GPS and streaming video going while talking to someone on your earpiece at the same time? Could be a runaway process, something whacky with something software related, something wrong with the battery, something wrong with the phone or something messed up with the charger. Since you plugged the phone in and didn't use a separate third party charger into which you plop the battery to charge, since the phone was involved, it's probably not the charger. My first guess would be something sketchy software-wise. The first thing I'd do is go into Settings > About phone > Battery use and seeing if anything looks crazy when it lists what software or functions are accounting for how much of the drain relative to each other. If something is burning juice harder than the screen, the good news is is that it might not be a hardware issue, might be something that could be solved with a soft reset. Could just have been a fluke. Can you recreate the problem? If you shut the phone completely off and it appears to charge without overheating, my guess is that the hardware is okay and there is no defect. And in that case, task management and auto-killing programs may be of interest.

By standalone and third party I meant one of those little cheapo things you plug into the wall, generally without any wiring, and you put the battery into it instead of charging the battery while it's in your phone. Unless it's the OEM, there is some small danger to using these things but the convenience and cheapness, if you use multiple batteries, may make it worth using anyway, though I'd keep your OEM battery away from it and only use cheap third parties in it.

I'm 80% sure that as long as your phone's involved, meaning the battery's in the phone and something is plugged into the phone to charge it, if you use a weaker charger .... no I'm not 80% sure, let me ask Telek first. But if you've got an outlet that packs a voltage that the charger is indicated to be able to handle, typically 110-220 volts or in that neighborhood, then it's just a matter of getting the thing plugged in (safely) whether you buy a cheap adapter or go nuts with paperclips.

When it's charging and discharging, that's two things heating it up, but I'd be surprised if a serious AC made enough of a difference to make it worth moving the phone to where you otherwise wouldn't mount it. In spite of the extra heat from also charging the phone, running it on a low charge is also not great for longevity purposes but I think, I'm speculating, outweighed by the heat. If your battery's running in excess of 40c, that's not an ideal situation, but hey, you gotta drive sometimes and not devote your life to air conditioning alignment and plugging and unplugging your car charger constantly. I've done enough speculating -- Telek's the expert on this, let him weigh in.