What has failed & what BIOS update does
I wasn't real clear with what the BIOS update did for sure, I thought the situation was like what Joe and Doug Glass thought, that the power supply was cooking itself. But based on the Toshiba pages, it's not a case of one of those little power bricks getting molten hot, it's basically a fault at the power supply connector in the laptop (Toshiba deems it a "harness failure"). I suppose it's got multiple temperature sensors, if there's not a sensor at the harness the BIOS can compare readings to tell if that portion of the machine is heating up more than the parts that normally heat up. If so, it somehow lunches the power supply, and then pops up the warning to have Toshiba repair it. I'm not impressed at them designing a power connector that melts, but I'm impressed at them for effectively implementing detection and protection for it.
"If the battery circuitry is simply drawing more than the supply is designed to provide, a BIOS update is not going to fix that. "
Actually battery charging rates are software controllable in a lot of cases -- Gateway had a specific battery exercise utility that'd fast-charge and fast drain the battery, and if you plug the normal Dell power brick into one the real nut burners, it'll chastise you at bootup for not using the 65W brick and then just trickle charges the battery instead of ramming that power back into the battery as fast as possible. It's highly likely Toshiba could cut power draw a bit, but I think this is a mechanical failure where reducing the current wouldn't extend the service life a bit.
Yeah... Toshiba. My dad has a satellite, which is pretty nice with Ubuntu 10.04 on it, but the store was unloading them for almost nothing because as shipped they were a basket case. They weren't shipped with Ubuntu, they shipped with Vista and 512MB of RAM, and an ATI chipset that is not XP compatible (no drivers for anything).