You know, there are tools specifically for exploring a browser cache... The browser has an index of the cache contents that usually includes MIME type as well as original URL.
I haven't used such a tool since the late 90's but I'm sure they still exist.
Here's a post that reviews browser cache viewer products for three major browsers
A quick search for more browser cache viewers turns up:
Here's another post about viewing the browser cache of Firefox.
If you are determined to do it the hard way, there is a computer forensic information site that lists some commercial tools for the purpose of "File viewer- to view and/or identify file format regardless of extension" for forensics purposes. It lists: Quick View Plus5, EnCase, Turbo Browser 98, DiskJockey 98" which I've never heard of and seem a bit dated, but many of the file formats in the browser cache were around 10 years ago.
Looking for modern and capable tool like that would be interesting. My searches didn't turn up anything amazing in this space. There are so-many file formats and this is such a specialized area, that it wouldn't really attract a shareware developer or an open source community. If these tools exist and are kept up to date with the latest format changes, my guess is that they will be priced appropriately for a forensic investigator's budget. (very expensive)
Again, you'd be better off approaching it using what the browser cache already knows about its contents rather than brute-forcing the naked files.