How to change the default location for temporary backup files on Linux?

Connect to the server via SSH.

Create a backup of Plesk variables' configuration file:

# cp -a /etc/psa/psa.conf{,.bkp}

Modify DUMP_TMP_D variable value in /etc/psa/psa.conf, so it will point to desired path:

# grep DUMP_TMP_D /etc/psa/psa.conf
DUMP_TMP_D /mnt/backupdrive/tmp

Set 1777/drwxrwxrwt permissions for the new directory:

# chmod 1777 /mnt/backupdrive/tmp

So that the result is as follows:

# ls -ld /mnt/backupdrive/tmp
drwxrwxrwt 53 root root 20480 Feb 8 21:39 /mnt/backupdrive/tmp