I recently built a new rig and went for AMD stuff (Phenom II X6 1090T, Gigabyte 870a-UD3, XFX Radeon 6870), all was fine for a week or so, but a few days ago I turned off the PC and when I turned it on again after some time the GFX card was howling like mad. Rebooting didn't help, so I open the case to check everything is ok, and it was. After a few more tries everything went back to normal... until I switched the PC off again. It seems each time I shut down and turn it on again after some time this happens. The weird thing is the longer it stays off, the longer the fan on the card spins full speed (or at least 70% or above).
I have tried various things, drivers, Bios settings, even editing the video bios and flashing, to no avail. Controlling the fan via CCC does not work either.
It does not seem like the card or it's fan is broken, when I finally get it running (usually by removing the card from the case and putting it back), it runs really nice until I power off again. Also, if I just reboot or power off for a short time, the issue is not present. Voltage issue maybe?
This card ought to be reasonably quiet, when it's idle at least. So there may be something wrong with the hardware.
Or it could be software. Download the latest version of CCC (if you don't have it already) and check out the temperature, activity and fan speed readouts in the performance tab next time you get the noise issue. This card should idle around mid-40s, with about 25% fan speed. If the activity is anything much above 0% when idle then something is wrong.
It might be worth noting I had a similar issue with this card, the fan would spool up when Windows (7, 64 bit) had a compatibility error (where the taskbar changes colour). If this is the case for you, try and close all programs that may not be fully compatible with windows 7.