Buying a 3rd party heatsink may be you best bet short term - I can tell you from experience - I have a friend that couldn't wait 2-3 days to get one from newegg (he was too cheap to pay for next day delivery), and insisted I "fix it". The bearings in the fan were shot, and the fan was making a big rattling noise. I cleaned the fan component with a lubricating oil (made sure to clean up the extra oil), and affixed a guard to keep the fan from spinning off the base.
He played games all night long, and about 4:00AM, the fan broke the guard, flew off, and he just kept on playing. His $400 GPU fried....It would have been cheaper to pay for expedited shipping.....
The moral of the story - don't bandaid things - replace them with proper...