I have my cache on the ram disk. For Firefox, you have to set up things in about:config.
Interesting entries include,
browser.cache.disk.capacity, you can shrink the cache here,
browser.cache.disk.parent_directory, point to somewhere you don't mind filling up, ram disk, etc.
browser.cache.disk.filesystem_reported, I seem to have set this previously.
Search for cache for other preferences while wondering why this stuff is no longer in the options.