For a very hands-on approach: Wink
With that tool it is possible to capture anything happening on the screen. Mark a certain area of the screen, set it to capture 30 frames a second and watch the video. This will require a lot of storage space and the result is an swf file.
Download the MP3 and use ffmpeg (or similar software) to mix the swf file with the mp3 into a file-format of your choosing.
Granted, this method is complicated (and hardly worth the effort), but it is really WYSIYG...
Another method is to find out if the player that this website uses buffers on your PC and if so, copy the buffer to a different location with software such as Unlocker. Convert the video later to your discretion. The trick here is to find the buffered data on your system.