Eric,
It may be interesting to swap their boards between them. Personally, I would start in the left card cage, with the LPU board.
Unfortunately my HP 9845B does exactly the same (I mean it remains frozen with "MEMORY TEST IN PROGRESS" on screen). My theory is, as the entire RAM (i.e. the leftmost boards) is accessible from both processors, perhaps it's the PPU (in the right card cage) who performs the whole memory test (this would also explain how come anything can be displayed at all), while the LPU may be completely faulty. To corroborate the theory, you can also withdraw the left ROM board (between the RAM and LPU). Obviously the LPU without its ROM is incapable of any testing -- and you still obtain a message on the screen, this time just a bit more cryptic.
I hope I will have another one here to attempt the board swapping within several weeks; perhaps I will learn more.
Anyway, I can hardly imagine any overheating after mere half a minute.
In case you succeeded isolating the trouble down to the board level, please let us know.
Regards,
Petr