"Thinking Tune" is track 13 of the album Arthur and Friends: The First Almost Real Not Live CD (or Tape). It is not actually a song, but is instead The Brain making noises of thinking set to music.
I, the Brain, will now engage in my favorite entertainment.
I like to think.
Hm-hmm. Ah. I like to think.
Ahhh. That was very satisfying.