I'm planning on buying a cbr1000rr c-abs in a month so i'm doing alot of research on the pros and cons and i found a problem similiar to yours being reported by owners all over the world!
Are you sure its due to heating??
Is your abs failure light flashing??
From what you've described, your riding in traffic and followed by parking and then when trying to switch it on, the battery seems to be drained and dead!
This being my first post, i dont know if i'm violating any rules by posting a link of another forum but just trying to help you out so here goes
C-ABS issues - Page 12 : Honda CBR 1000RR Motorcycle Forums: 1000RR.net
2010 cbr1000rr Fireblade ABS Question
try reading through the above forums and you'll figure out what the problem is! honda japan have officially sent this email to an owner who's experiencing the same problems as you...
After many calls to Honda Japan and Europe to find out what is wrong they came back with this explanation:
"Below 6mph the ABS is active, but not calibrated - once you go over 6mph, the system does all its checks and self diagnosis etc.
When you drop down below 6mph, to park for example, the system cannot self diagnose itself. This causes a problem when you need to get the bike into a tight parking spot or awkward garage where you may go in and out a couple of times to get the angle right.
As the front and rear wheels are moving at different speeds when you turn the bars back and fourth, it tricks the system into thinking a wheel needs ABS pressure and therefore applies a little power where it thinks it needs it. This is not noticeable when you are moving it around.
However, even AFTER you cut the ignition, the system stays active and drains your batt in 30 mins"
i maybe wrong but its worth a try reading through those forums!