I think the cooler can be removed without too many problems.
I have seen this discussed before, mostly by some of the guys in the US where the temperatures tend to be a bit hotter than here.
I could only find a couple of relevant threads though, there are more but I dont have time to trawl through them.
http://www.ducatimonsterforum.org/in...?topic=60700.0
http://www.ducatimonsterforum.org/in...?topic=55884.0