Yes white reflects the heat helping the piston to remain cooler... black heads on snowmobile engines reduced temperatures 40 years ago.
These two situations are entirely different. The white ceramic coated piston is reflecting heat so as to not absorb it in the first place. The white ceramic coated piston is exposed to extremes of visible light (flame inside the cylinder) for 1/4 or 1/2 of it's operating time, (2 or 4 stroke). That is not the case with the exterior of the heads. The reasons for these two situations are not even closely related to each other, and while the paint idea can apply to gun barrels, it is not for the reasons suggested by a few folks in this thread.
Folks should differentiate between heat radiation, and heat absorption. The SUN makes heat and transmits it in the form of visible light energy (and plenty as ir as well). Visible color of an item will absolutely affect how well it will absorb that heat energy because it is in the visible spectrum. Its color will NOT affect how well it will give that heat back off as radiated heat. Again, till it's red hot. Its color will also not affect how well it will absorb the IR energy from the sun.
So, you could think of it like this. If you have a 300 Degree F item in a room, will it cease to cool off because you turn the lights off? Other than the heat energy it picks up from that light, will the light have any effect whatsoever on the item? No.
Now, with the lights off, paint the item 5 different colors with otherwise identical paint. Will that make any difference in how fast the item cools. No. The only difference it will make is if the paint is a better or worse conductor of IR heat. If the paint is a better conductor, it will cool faster. If the paint is worse, it will cool slower.
I suspect the temperatures of operating engines is so much above sustained barrel temperatures that what works for engines won't be as effective for barrels.
As I said above, till the item is so hot it begins to give off light, it's color is irrelevant.
Another great way to think of this is to think about sunblock. SPF90 or whatever. This stuff does not insulate from heat to any measure, if it's hot outside, you get hot. It doesn't block light to any degree, your skin is still highly visible, just as much so as it was before you put the sunblock on. But, it does block Ultraviolet, a form of energy you cannot see. Again, no effect on the visible light spectrum, much effect on the UV spectrum.
Plexiglas is a great example of a substance that is virtually opaque to IR, yet transparent to visible light. Two different energies.