Sure it ran out of inodes and it isn't that /tmp is a ramdisk/tmpfs and only small? - you can change the session path in your php.ini by changing/setting session.save_path.
If inodes are the problem, you could also store php sessions in memcached - a google search will give you loads of instructions on this, eg: http://www.dotdeb.org/2008/08/25/storing-your-php-sessions-u...
If that is the problem mise is facing, you can swap out the storage that PHP uses for sessions (to use something other than files), I'd point out the relevant docs but I have a meeting to get to.