First create a temporary directory somewhere with more space. Let's call this /home/tmp for the sake of example.
If you login in single-user mode, you can delete (rm -rf) the tmp directory. You can then create a symbolic link to the new directory with:
ln -s /root/tmp /home/tmp
This effectively remaps the /root/tmp directory to /home/tmp.
Another alternative is to mount another partition onto /root/tmp, possibly a tmpfs partition (tmpfs is held in memory, is not preserved between reboots, and doesn't need a physical partition. But it does tend to eat up RAM). I think that's:
rm -rf /root/tmp/*
mount /root/tmp -t tmpfs
This will allow you to store whatever you like in /root/tmp without eating up space on /.
By the way, I've assumed that you meant /root/tmp as you said, and didn't use /root to mean “the root directory” (i.e.
/) If not, replace all /root/ with just / in the above.