> Reallocated sector count is 880. The temperature stays above 50°C. Is this a hard drive failure?

880 reallocated sectors is a sufficient reason to replace the dying disk.

For a rotating hard drive 50°C is already dangerously near the maximum allowed temperature. That temperature is increasing wear.

What is your ambient temperature?
You should provide cooling for your drive to make your disk approach a hopefully much lower ambient temperature instead of heading towards the maximum allowed temperature.

If a possible successor of your drive is being put in that thermal environment, he won't live long.

> Try to format the disk using a slow (not quick) format, which will rewrite all the sectors. Check the

Any variation of a window format command will delete stuff on the drive.
This is a irresponsible hint!