ok, from all the ideas, here's my opinions:

NO, Don't take the cover off, you can paint it if you like, i did to my girl in blue high temp paint, still works fine (6 mo.)

Why? ewww..... a lot of heat, not a good Idea. My cousins told me that the cover shouldn't taken off. He orks with car for 30 yrs and he knows.

so my best bet is NO, just paint it how u like it