With no heat sink at all, the chip will over heat pretty much instantly. Even at startup.
Heh - anyone remember the videos showing what happened to Athlon XP's without a heatsink?
However, I would have thought that the minimum power consumption tendencies of many modern GPUs would make them significantly less likely to overheat during startup. I don't know whether the 280X has those sorts of capabilities though, and also who says that resuming from S3 or the initial boot stages
is easy-going on a GPU. Considering how many CPUs act (or used to, unsure) during the BIOS stage (ie. high power usage), perhaps GPUs do similar things.
The GeForce 6200 in my mum's desktop was a ah heck to nail down as the cause of stability issues. Again it was intermittent, and never under load. It would just decide, seemingly randomly, to start acting flaky. I tested everything else I could think of before swapping out the card.