I doubt it's the 3870 causing your machine to turn off, because it simply can't. You'll either get a lock-up or a bluescreen
afaik. These cards can take over 100C fine, confirmed by the manufacturers. I'd look into problems with your CPU cooling
tbh, its more than likely that an option is set in the BIOS to turn the machine off when the CPU temp gets to a certain degrees.
Anyhow, Rivatuner can sort out fan speed for you.
I'm currently using a 3850 Pro - 63C idle, 93C load.
If I force a fan speed of 50%, it sits at 54C idle and hits about 73C load at 730/2000.