It likely means if you care about what is on the drive you should immediately make a drive image backup
as quickly as possible.
You can then download the HDD maker's free diagnostic app from their support page and test the drive. If it does not report temperature you can install HWMonitor which will usually supply min/max/current temp range for drive. I am not sure what removing the drive from the case for a while has to do with your issue.
Likely the drive is bad. But it could be the SATA data or power cable, SATA controller. Very unlikely case cooling especially in a tower. Also possible if using screws to mount hard drive they are too long and pressing into housing...they would then expand as the system and area heats up pressing further against the housing and when you remove you relieve pressure and allow a new round of failure (uncommon).