First off, as ScottALot alluded to, black absorbs light in the visible spectrum whereas white will reflect visible light. Infrared radiation, on the other had, which I believe you're refering to as heat, is often equally absorbed (and emitted due to Kirchoff's law) by both white and black materials. For example, white and black electrical tape both have emissivities/absortivities of ~0.90-0.95. As for the point about black cases being bad, if you're relying on radiative heat transfer for cooling in your case then you definitely have a problem. Copper and aluminum heat exchangers have very low emissivities so the hottest components emit head least efficiently.
In english for everyone else: Small scale like a computer a black case will not affect temperatures negatively due to the low amount of visible light that will be absorbed to the case, let alone the fact that most interior lighting is relatively low intensity. However, in larger scale such as say, a car in the sunlight, a black car will have higher temperatures than say, a white car(this has been tested a few times by multiple places and confirmed accurate). Not to mention, the purpose of a computer chassis is not to
Key pieces of advice when painting(somewhat repeated as what g25racer mentioned):
1. Sand! Sand! Sand! Cannot stress this enough, as paint does not stick well to the galvanized zinc surface of a computer case interior, get as much of the zinc layer off as possible. I recommend using either a 320 or 400 grit wet or dry sandpaper for this step. If you have access to a media blaster, that is an even better option.
2. Wipe it down like g25 mentioned, acetone is best here, rubbing alcohol will work however.
3. Get a self etching primer, put a few light coats on.
4. Get a good quality spray paint, something such as krylon fusion although meant for plastics works excellent on computer cases, rustoleum is also an excellent choice.
5. Let the paint dry fully between coats, dont try to cover everything perfectly on the first coat, multiple thin coats will result in far better looks.
6. Let the final coat dry for at least a week, then wipe everything down with rubbing alcohol and apply a final coat, allowing the final coat to dry for at least 24 if not 48 hours in a well ventilated environment.