Heat Transfer

Fins increase the surface area for better heat transfer. The black colored paint on the radiator is a high heat paint. Black being the color that is produce in the most abundance. The most important reason that I can think of is cosmetic. Any other color would standout and take away from the chrome on the grill and would have to be of a color that did not clash with the car's exterior paint.

Car radiators are forced convection heat exchangers. There is almost no radiation involved. The tubes carry hot water and need to be able to efficiently conduct that heat to the outside; thus, they are good conductors such as copper or aluminum.

When the heat reaches the outside of the tube, it needs to be carried away by the moving air and you get the greatest efficiency by having fins that are spaced far enough apart as to permit air movement. Getting the most such fins in the space available results in thin, fairly short fins. Plus, they're economical to manufacture.

The radiator tubes need to be free of oxidation (which is typically a good thermal insulator), so the economical choice is to paint or anodize them. Since the fins are already attached, they get the same treatment.

The most economical (and the best to go with other colors) is black.

It's about 99.7% economics.

While I agree that the majority of heat transfer from a radiator is actually by conduction, the black paint increases the radiator's radiative heat dissipation. Any time a body is at a higher temperature than its surroundings, it will radiate heat away. Black is the most efficient colour for this (hence the term 'black body radiation').

Truth be told, a radiator really should be called a conductor!

At the temperature of auto coolant, almost any color can be used to achieve the same radiation emissivity. Emissivity is different for visible wavelengths from that of low temperature heat wavelengths. Think of semiconductor heat sinks - blue, red, gold all work about as well as black.

But, radiation (and conduction) have very little to do with how a car radiator works. Just fire up a Crown Vic with the fan disabled and let it idle for a few minutes and you can see it overheat. In fact, if you want to let a big engine like that idle, some folks crack the hood about an inch or so to reduce back pressure on the fan flow.