Laptop's HD is making grinding noises and clearly dying. Please advise on heat / turning off strategies as I try to help it survive last backups?

I have okay backups and as we speak I’m improving them (getting everything else I care about off the drive). Laptop is running pretty hot although room’s ambient temp is 76. I’m asking here your opinion re. whether I should steadily keep copying in hope of getting as much data off as possible, or shut down periodically to let my machine cool off. I think the drive might not spin up again if I shut down (the noises it’s making are pretty tortured and are changing rapidly). Thanks for all advice.