Short Explanation (IF YOU DON"T UNDERSTAND THE VIDEO, READ PLS^^)
Just find all the vid's pieces in "Cache" or "Media Cache" folders, copy them to an empty folder, navigate to that folder via your console and use "copy /b * wholevid.mp4" command.
The idea is to find all the vid's pieces Chrome cached on your local drive and glue them back together into a vid. Though this approach works perfectly with Chromes's "Media Cache" folder, it doesn't work that well for Chromes "Cache" folder. The video can be played back but it seems like it's header is missing or something like that.
Additional info you probably would want to know or not
Chrome has 3 folders on your disk it keeps stuff in. They are: Cache, Media Cache, Pepper Data.
The last one is used only for Flash(*.flv). Vids are stored as singular files with *.tmp extensions. Basically. just wait for a vid to load, copy and rename that file.
"Cache" folder stores both pictures and vids, but in fragments(multiple tiny files). I think vids fragments are in a form of 'stream' and have no header because each fragment is an independent video on it's own. You can stitch those pieces back together (as I showed in this utube video) and play them back in any video player though the result you get is not an actual 'normal' video file and some online video upload servisec might not accept it at all(not utube though).
"Media Cache" stores only videos. They are fragmented into multiple files, as well as in Cache folder, but with preserved internal structure which enables us to put it back together exactly as it was.