When running firefox, in the Preferences, you can clear your history, set a limit for offline storage, and clear your offline storage. Also look at your ~/.thumbnails/ directory. You may be able to free space there.
If /tmp & /home are directories of the root partition (/) and /home isn't on it's own partition, you could delete contents you own before powering down. You may find an option where you can configure your system to do this automatically when you reboot.