I battled this problem for a user today, and found a solution that may work for others.
Our scenario was:
FCPX (10.2.3) libraries were stored on an external drive, and backed up with Time Machine to another external drive.
The video drive failed. We purchased a new drive and wanted to use it as the Time Machine drive, as it was now the largest drive.
We copied the TM backup to the new drive via the Finder.
We formatted the old TM drive to use as the new video drive, and copied the backup files to it via the Finder.
After doing this, we got the ".fcpcache.tmp couldn't be removed" error message for almost all FCPX libraries on the drive.
Restoring the folder that contained the libraries via the TM interface instead of via the Finder made most of the libraries work again, but not all.
Ownership settings looked correct for these files, but they couldn't be renamed or deleted without entering an administrator password, and they couldn't be moved from their locations, only copied.
Our method of moving the TM backups and files around via the Finder may have contributed to the problem, but I've seen reports of people having this issue when using TM in the typical way.
Here is the fix that worked for us:
Download BatChmod from https://www.lagentesoft.com/batchmod/.
Open one of the affected files in BatChmod.
Uncheck "Change ownership and privileges". (I did this because ownership looked correct and I wanted to limit was I was changing, both to help identify the problem/solution and to avoid accidentally messing anything up. Leaving it checked would probably be fine.)
Check "Clear ACLs".
Click Apply.
After clearing the ACLs, the files would open in Final Cut Pro X without complaint, and renaming/deleting/moving worked correctly in the Finder as well.
Somehow the ACLs on these files were causing problems after being restored from the Time Machine backup, and removing them got rid of the problems. This can also be accomplished via the Terminal, but I prefer to work with GUI utilities when possible.
Hope this can help others with this issue!