Unfortunately there is no add-on for this for Firefox but however you can screen your whole desktop and use Firefox instead of Chrome.

See Mirroring your full desktop via this link: http://www.gizmag.com/5-ways-to-get-more-out-of-google-chromecast/29125/

DISCLAIMER: The above-mentioned URL would take you to a non-Mozilla Web site. Mozilla does not control it and is not responsible for information outside of Mozilla web sites.

The link leads to a page all about using Google Chromecast, but not one word about how "you can screen your whole desktop and use Firefox instead of Chrome. ".

@moborisn "[...] but not one word about [...]"

It does and it doesn't. Look for "Mirror Your Full Desktop". That's another way to say "screen your whole desktop", the first part of your quoted text, and that includes "and use Firefox". What the feature doesn't exactly allow is "instead of Chrome".

You still need to install Chrome, at present. There's no way around that until someone develops an extension/plugin/whatever for Firefox. But once you start Chrome and mirror the whole screen, you can use Firefox for all your "real work" -- no need to use Chrome for anything other than starting the screen casting.

(This website <http://stackoverflow.com/questions/17967442/convert-google-chrome-extension-to-firefox> says that a conversion should be possible for a programmer. A website called extensionfactory has been touted in places, but its conversion pages seem to be gone when I checked just now. It inspired me to look for other efforts, but I haven't found any.)