Try re-flashing the BIOS. There's actually two BIOS on the 5970, one for the master GPU and one for the slave GPU. Make sure you flash the correct BIOS to the correct GPU.
Been a while since I've ran 5970s, but this post helped me when I re-flashed mine:
http://forums.bit-tech.net/showthread.php?t=185918
I used the "800/1100 1.15v VDDC 1.15v VDDCI" BIOS found on that page, but you don't have to use one of those. The brand doesn't matter, by the way; AFAIK there were no OEM-design 5970s, they're all reference design, so a BIOS from any vendor will work. Before using the BIOS found on that page, I was running a Sapphire BIOS on an original ATi card (one actually manufactured by ATi, not produced by an OEM.)
If re-flashing the BIOS doesn't help then you might have a faulty temperature sensor or some other hardware malfunction.
Been a while since I've ran 5970s, but this post helped me when I re-flashed mine:
http://forums.bit-tech.net/showthread.php?t=185918
I used the "800/1100 1.15v VDDC 1.15v VDDCI" BIOS found on that page, but you don't have to use one of those. The brand doesn't matter, by the way; AFAIK there were no OEM-design 5970s, they're all reference design, so a BIOS from any vendor will work. Before using the BIOS found on that page, I was running a Sapphire BIOS on an original ATi card (one actually manufactured by ATi, not produced by an OEM.)
If re-flashing the BIOS doesn't help then you might have a faulty temperature sensor or some other hardware malfunction.