Put the drive into an airtight bag, like a Ziploc bag, or wrap it TIGHTLY in plastic wrap or a garbage bag, THEN wrap the entire thing in a medium-size towel, and place it in your freezer for 20 minutes.
The idea is that you want to see if deep-cooling it QUICKLY will allow it to run one more time. You do NOT want to FREEZE it, because as it THAWS, you'll have condensation INSIDE the drive, and the water will probably cause many problems, so do NOT leave it in the freezer for more than 30 minutes at MOST.
I actually tried this trick with a friend; his drive died, and we could NOT get it to work, even after leaving it in the freezer for 30 minutes, BUT, he later told me that he DID have success doing the same thing while visiting family members who were having problems with their system.
If it works, you'll get one last BRIEF chance to retrieve some data; if it doesn't work, you'll be no worse off than you are right now.