It might be worth the trouble to remove and re-insert the video card into the same PCIe socket. If there is a second PCIe socket on the motherboard, give that one a try too. Otherwise, it sounds like a defective fan on the GPU. Sometimes you can add another fan to blow air across the motherboard (and onto the GPU) to provide more airflow or even take the side of the case off temporarily until you can fix the fan issue.
As Albert Einstein said, "I could have done so much more with a Big Al's Computer!".