Since you are have about a minute before your HDD "warms up" and crashes, the best thing to do is cool it way down by the "freezer method". Put it in a zip lock bag, add one of the drying agent packets like you find in vitamins or medication bottles, and push the air out and seal it. Put it in the freezer over night. Take it out, connect it immediately to a data and power cable and boot up your computer. Have your system ready to copy all your data over to a good HDD immediately. Hopefully you will get 30 minutes time to back that data up rather than just the 1 minute now.