Where do Java Applets live?
I remember a recent SO answer that mentioned that Windows does clever stuff to obfuscate the real file names and locations of temporary internet files. I believe that this is an attempt to make life hard for malware. That would explain why the file does not show up in a search.
As @leonm says, if you just want to get hold of the applet JAR file, why not just read the HTML file, find the link to the applet and download it using
wget or an equivalent tool.
If youre interested in algorithm of code that isnt obviously available you should contact the author of the applet.
Please be careful as decompiling to copy algorithms is usually covered by copyrights and other laws.