As you bought a used card, I would suggest you take the heatsink off and re-seat with some new thermal paste. It does sound like your gfx is overheating and I reckon doing this will bring your temps down significantly.
For example, I recently bought my dad a used Asus HD3870, plonked it in and tried a few games, played Grid with all the eye candy turned on and it played for a couple of minutes then locked up the whole machine. Re-booted, and monitored the temps doing the same thing and they went up to ~95c before I stopped it and pulled the card out. I took the heatsink off and the old thermal paste just flaked off. The paste hardens over time and I suspect where it had been in transit the vibrations had cracked it off the surface of the GPU allowing it to get much hotter than normal.
I replaced the thermal paste and after it had been run in for a bit the same card only hits 78c after 10 mins of Furmark.