I remembered reading something about the fans on one of the MSI Twin Frozr cards, so I went to the Newegg page for your card and read the user reviews.
Lots of dead fans. A quick internet search shows me the fans are very effective, but very
infamous for having a short life span.
Bad news and good news. First, MSI it seems does not cover fan life in the warranty and will charge you for replacing them. In addition, they cannot replace that GPU as they don't have them in stock any longer, one guy was offered a reference card as a replacement. You can replace them yourself, but it's tricky.
The good news is you can get new fans for it for between $10 - $20 from various online retailers. There are detailed instructions (like in that link) on how to replace them, and youtube videos that go into detail for that model.
My opinion is this is what your issue is, when you mentioned that sound it made me remember reading about this. I don't think flashing a new bios will fix it, but it's worth a try. You can also contact MSI support and ask permission to flash a new bios without voiding the warranty, one guy in the Newegg reviews did just that. Use the support numbers and email addresses on that Newegg review page from the reviews to contact them. Good luck.