Heat is often a factor in drive failures, so I suggest letting it cool down, before trying to back up the data from it. Some say that cooling a drive in the fridge or freezer gives you more uptime, though I haven't tried that myself.
I had a situation early last year where I thought an internal 250GB SATA drive was failing. It was making clunking noises and dropping offline under load. As a last-ditch attempt to see if I could salvage it, I wiped it with a low-level utility (from the manufacturer) and reformatted it. That was a year ago, and it's still going strong, with no weirdness. I think that it was able to map out bad sectors when I reformatted it, and therefore didn't try to access them ever again.