mysqldump: Error: 'Can't create/write to file

Perhaps you can change the owner with

chown -R mysql:mysql /var/tmp

Check to see if there is a [mysqldump] header in /etc/my.cnf. It may look like this:

[mysqldump]
tmpdir=/var/tmp

or perhaps under the [mysqld] header

[mysqldump]
tmpdir=/var/tmp

Try commenting it out and trying mysqldump again.