How can I see Explorer.exe's frames per second?

explorer.exe doesn't really control the whole visual presentation of your desktop, per se. It runs the shell (things like the start menu and task bar, file and folder icons, etc), but it doesn't have much to do with video rendering. The closest thing to that would probably be dwm.exe -- the Desktop Window Manager that composites the graphics of all the programs running on your desktop together and sends them to the video driver.

I'm not actually sure of a way to look at the framerate of the desktop in Windows, but you don't need to -- it is basically always running at the refresh rate of your monitor, ever since the Desktop Window Manager was introduced in Windows Vista. The design of this is basically that all the programs update off-screen copies of the screen as fast as possible, and the DWM copies the current changes to the video driver once per screen refresh. Because this drawing process works differently from the way discrete video frames are generated in most games, there isn't really an "FPS" number you can associate with it, at least not in a sense that would be comparable to what we think of when we think of FPS in games.