Discussion, talk and tips
https://forum.puppylinux.com/
You can't set this in preferences anymore but you are supposed to be able to set it in about:config. The default value there is 256000 (which I suppose is 256MB) but this definitely does not work. Last time I checked my cache was close to 500MB in size. This is something that Firefox has messed up with the newer versions.
Mine is 11 KB at the moment. I've configured firefox to delete the cache at exit. This option is in the settings under history.
If you keep the browser opened all the time, maybe setting browser.cache.disk.smart_size.enabled to false can help. Found it by searching for the topic title but it's hard to test with a such small cache.
(about:cache shows the current size of the cache.)
@amethyst :-
It's true. Mozilla no longer give you fine-grained, fully manual control of your cache size any more. What they have implemented is a near-as-dammit identical system to that of the Chromium-based browsers, where you get the "option" to periodically clear data out of the way.
As far as Mozilla are concerned, they haven't 'messed-up' at all. To them, this is a giant leap forward, because it's yet another step closer to being able to compete with their arch-rivals on a level playing field. But as with previous major changes, this particular advance is guaranteed to annoy those who preferred the older method of full manual control......usually folks running older hardware, more often than not with limited resources.
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It's an uncomfortable fact of modern life; it doesn't make a scrap of difference how much RAM and/or storage vendors make hardware capable of supporting. Purveyors of software seem determined they're going to make full use of every resource you possess, regardless of how much (or how little) that may be.....
It encourages scrappy, untidy, 'lazy' coding.....because programmers are getting to the stage where they no longer have to concern themselves with keeping their code neat'n'tidy. Limitless resources, don'tcha know..?? ("Let's use it..!!") 
And I fully agree with the OP in burunduk's link, above:-
"I realize that many website developers these days are enamored with the bells, whistles and flashy graphics needed to gain eyeballs and earn something from clicks and click-throughs, but the present-day notion of some endless user supply of RAM grates quite hard with someone of my vintage and experience with computers since the late 1960s."
Mike. 
chmod -R 444 /path/to/cache
maybe setting browser.cache.disk.smart_size.enabled to false
I'll try this...