Is there an extension for Firefox which I could use to schedule so that FF would clear the cache every x minutes or hours?
Afaik, cached files are stored in a Cach-dir, in a hidden dir in your home.
find /home/eidylon/.mozilla/firefox/*.default/Cache/ -mmin +120
would find files there, older than 120 minutes. With a switch -delete you would get rid of all the older files:
find /home/eidylon/.mozilla/firefox/*.default/Cache/ -mmin +120 -delete
but don't hurry, I didn't investigate some files, which seem to be meta-files:
find /home/stefan/.mozilla/firefox/*.default/Cache/ -name "_CACHE_*" -printf "%f\n" _CACHE_001_ _CACHE_002_ _CACHE_003_ _CACHE_MAP_
maybe they need to be in sync, so you should do an backup, before testing what happens on deletion. The files seem to be partly binary, and not trivial to understand.
If all goes well, you can write the command to your crontab with
for repeated cache-cleanings.
The Cache Status extension could do the trick for you