I had what sounds like a similar problem a year or so back.
Temperatures looked OK, but I replaced the thermal paste anyway with Arctic Silver. It made no difference.
I was using the latest driver, so I tried going back driver versions, eventually reinstalling the driver from the supplied CD. No cure there, so it wasn't a driver issue.
After a month or so, the problem started appearing on the desktop as well. Not as severe, but a sort of rip across the screen every few minutes.
This period also coincided with some random computer crashes, which puzzled me, but as Windows 7 and onwards uses the GPU for some desktop processing, it makes some sense that a failing GPU could take down the whole OS.
Underclocking the card by circa 20% made the problems go away for a couple of months, but slowly they came back until one day, we achieved catastrophic failure, and I had just static when I turned the computer on.
If your card/computer is within warranty, then it's a no brainer. Get the supplier to swap out for a new card, or perhaps, depending on the warranty terms, a whole replacement computer, or repair.
Otherwise, based on my experience, you'll be buying a new graphics card sooner rather than later.
