I have had some problems with my ASUS 6870's. My problem wat the cooling didn't start soon enough. Had exact same problems like you describe.
Use the Radeon tools to set the fan speed higher (50% or so) and check your temperatures on a second display. I guess there is your problem.
The problem i had in detail:
The driver was set to a manual fan speed.
When i starten BF3 the
fans tried to spin up but didnt (becouse they where set to manual).
I did a clean install of the drivers but still the same problem.
Then i found out about the fan settings. Now i set them to manual when i start playing a game.
Result, no more problems.
Highest temperatures i got with 1 of my cards was 103 degrees Celsius...... :S
Good luck and let me know what your card does with the manual fan speed settings and his temps.