Sounds like the Fan's bearing is bad. See if the GPU's manufacturer can send you another shroud or fan to replace it under warranty.
I was using a VisionTek HD 7850 when two of the GPU's fan blades broke which caused the GPU card to run hot. I emailed Visiontek Support about the specs (dimensions) of the GPU card's Fan to replace it myself. They said that the card has a limited Lifetime warranty but in my case it was voided because my GPU card was too close to another card on my motherboard. But they said since I was a customer of Visiontek they would send me a new Shroud free of charge even though it was not covered due to the warranty be voided. The new shroud was the entire cover with the heatsink and fan. I replaced the Shroud (GPU Cover) and the GPU card was good as new. I needed to reapply Thermal paste to replace the entire cover though.
agree with elstaci, fan noise is almost always a problem with the fan itself, I had that problem on an HP elitebook, and found a replacement on ebay for 7 bucks, a fairly easy install (a solution for those out of warranty)
Different units vary in difficulty, had a dell laptop that was almost impossible to get at the fan, fortunately, the elitebook was pretty easy, downloading a service manual should give you a pretty good idea of what you're looking at, if you go that route
ever since, I keep a can of computer air, and blast the area about once a month, so the fan doesn't have to work as hard