You can give it a shot and see if it works, seems it should.
In Terminal type each of the following comands (in red) followed by a return.
cd /private
sudo -s (you'll be prompted for your admin password)
mkdir tmp
tmp is owned by root and the group is wheel
So after you create tmp as root (the sudo -s makes you root) your new folder should have wheel as the group, a test directory on mine does.
Now set the permissions
chmod 777 tmp
chmod +t tmp (special for tmp, only the file owner can delete a file)
That should do it.
Type exit to quit sudo -s and drop back to your admin user.
ls -al should show the permissions as follows...
drwxrwxrwt 186 root wheel 6324 Jan 25 09:49 tmp
You will now have a new tmp directory. I have no idea how long your system will take to populate it with the stuff it normally jams in there. The system could be kind of wonky till it gets back to normal.
