Start playing some tunes on Pandora Radio, while keeping Pandora streaming go to your temporary folder (on Windows type %TEMP% in a run dialog, on Linux and Mac OS it's /tmp) and look in /plugtmp. All the access-# files (WebKitPlugInStream-# files on Mac OS) are MP3 files cached from Pandora.

(edit:
If you can't find this folder in your temp folder, try your browser's cache folder.
For Internet Explorer, this is C:\Documents and Settings\[Windows username]\Local Settings\Temporary Internet Files and the folders within it by default.
For Firefox, this is in /Cache in your profile folder.

Still no luck? Try performing a file search on your hard drive(s) for access* (WebKitPlugInStream* on Mac OS).
)