I saw a new 2009 Ducati Monster at the dealer and was somewhat disappointed. What Ducati did was move everything out of sight. That big radiator, gone, the cool oil cooler, gone!
I'm sure the '09 Duc has these things and there is some evidence that they exist. I suspect the radiator(s) reside in the little black plastic box that is located just below the red trellis portion of the frame.
This bike was a "naked" bike, that means that nothing was hidden behind body work. By hiding all the components Ducati has made a different bike and to my mind, not as attractive.