i don't know much about video but ii know how streaming audio caches and it should be the same ith video; like alain has said, streaming media can't be decoded from netscape-tye cache.. so it is downloaded to the temp folder, normally with a tmp extension.. copying the stream file is very hard with mozilla browsers because they lock the file whilst the file is playing and if you close the browser or window the file will be deleted immediately.. so you need some kind of utility that uses windows disk service to copy locked files.. like hobocopy or shadow copy etc.. it's very tedious and not always successful, not to mention that some streaming sites zeros off the file once it completes loading it..so copying the complete file requires timing precision.
what i normally do is i send the page to ietab or you can use internet explorer for that mission because ie does not lock the file from copying while it's streaming.
in ietab/ie the file will be loaded normally from ie's cache "temporary internet files" and not the temp folder.. however in most cases, the file will not have a tmp extension like in mozilla..it will either have no extension atall or have a bogus familiar extension(image,html,php etc) to throw you off so locating it isn't very easy especially when you have a big cache.
first empty ie cache before going to the site with ietab so there won't be many files to look through.. load the site and go to ie temporary internet files folder.. the file will have a bigger size than normal cache files and most importantly it will keep growing as the site loads the video/audio so this should help identify it..right click on the file you suspect(do not drag and drop) and select copy..now go to the folder where you want to save that file and right click and paste..once the file is copied, use a file identifier like trid(http://mark0.net/soft-trid-e.html) to know its format (flv, m4a, mp3) so you know what player to use or what program to use to convert it to the format you prefer..
the next step is to ensure that the file you've copied has completed and not partial.. monitor the site where the media is streamed, the flash player will have a progress bar.. right before it reaches the end(depending on your connection:when there's only few seconds left).. right click and select paste again in you destination folder.. the file should have completed or just have a couple seconds off.. this will not affect the integrity of the file as most media files(avi is one exception) will play normally with 1 or 2 seconds chopped off at the end.
you can test and practise with this file:
http://www.imeem.com/people/hmSPdL7/music/kJRd9qIn/suzanne-vega-obvious-question/
hint: the file will have a gif extension.