I paint computer cases all the time.
Just use a good quality spray enamel (Painters Choice, Krylon, etc). Do Not use Lacquers as they will attack the current paint and may damage plastics. Disassemble the panels, sand first, wipe with a damp cloth, let dry and go for it. 2 or 3 light coats, 3 or 4 hours between coats and you can have a real nice looking case.
It's not going to affect heat dissipation... It's a common myth that cases dissipate heat... if anything they hold it in a small area, that's what all the fans are about.
--->It ain't better if it don't work<---