My data point, the other Toshiba laptop I have is a C650D, serial number 7A247044Q
Battery SN is a 6F5100J83A1AAN rev 1.00 V000210180 D/C J0070
Its been quadded with P720 (15W) and also has the thermal mod and runs a *lot* cooler now with fewer glitches.
The graphics chip on this one has clear signs of overheating so this hopefully prevented some damage as before it ran for about half an hour before graphics glitches began showing up.
Just a thought however, some models let you install a non stock battery (ie high capacity) and also many models have one battery between 3 or even more base configurations differing only by screen size and hard drive/memory capacity so this might be a bigger issue than at first glance.