We all know that black absorbs heat better than white or the lighter colours, but which colour, if any, radiates heat the best ?
Darker colors get hotter than lighter colors, because they absorb more light and heat up from the extra energy, but this would not affect that rate at which they radiate that heat.
There’s not going to be a unique answer to your question, because there is no unique spectral makeup to the colors we see – the apparently same color red can be made up of an infinite number of combinations of spectra, ranging from a sharp lin at one wavelength to a pair of spectral lines all the way to a coninuum of wavelengths that “add up” to the same red.
In fact, since a lot of EM radiation os in the infrared and ultraviolet, you can get essentially the same efficiency from teo different colors that act as perfect blackbodies in the invisible part of the spectrum.
At any given wavelength the absorption and radiation are symmetric - good at adsorbing, equally good at radiating. What confuses matters is when the energy comes in at one wavelength and leaves at another.
The answer to the OP is simple. Black. Make an object black at the wavelengths you want it to be good at radiating at, and it will be as good as it is possible to be. Now what colour it appears to be in the visible wavelengths matters not so much - so long as this isn’t the wavelength of interest. In general if something has any colour it must be reflecting light of that colour, and thus it is not efficient at radiating that colour (where the colour is the spectral mix of wavelengths it reflects.) If you are worried about objects that are at ordinary terrestrial temperatures the wavelengths you are worried about are in the far infra red. There is not a great correlation between visual colours and reflectance at those wavelengths. So there is no answer to the OP if colour is defined as a human visual colour. But if you define colour as the reflectance spectra of the object in the IR, the answer is black. Always.
Colour is a visible issue- mostly a matter of reflection vs. absorption of visible light - and doesn’t necessarily have anything to do with heat radiation (which is usually invisible unless something is very hot).
As others said - a surface that looks dark in the infrared wavelengths will radiate heat most efficiently. This parameter is called emissivity; the higher the number, the better it radiates heat, with 1.0 being a perfect blackbody. You can find tables listing emissivity for different materials (example).
Most everyday objects have fairly high emissivity. (Note, for example, that black paint has only 11% better emissivity than white paint.) The major exception is shiny metals, but only if it’s clean, not oxidized, and not coated.
If something is black because it has carbon black in it, as very many manufactured black finishes do, then it will have an emissivity near one. But some black things such as magic marker ink are not based on carbon black, and may not be so good. Human skin is also nearly one, regardless of its visible color.
For a given wavelength, the ability to absorb radiation is equal to the ability to radiate. So if a particular surface is 50% efficient at absorbing infrared (i.e. absorbs 50% of incident infrared radiation), then it will be 50% efficient at emitting infrared (i.e. it will emit 50% as much radiation as a perfect blackbody).
If that weren’t the case, the object would absorb more (or less) radiation than it emits, and eventually end up in an equilibrium temperature that is hotter (or cooler) than the surroundings. Which would be a violation of the laws of thermodynamics.
Would an internal combustion engine painted black radiate heat more efficiently than painted in any other color? I do know that chrome coatings hold heat in.
Yes, if by “black” you mean “black in the infrared”, which may or may not be black in visible light.
Once it is black, you may find different black paints are slightly better than others because of their pigment makeup which may affect their emissivity in the infra-red. A paint based on carbon-black or some iron oxides will be very effective. These are good for engine paints anyway as they are resistant to high temperatures, so very likely what you would get even without asking.
Also, for an engine, radiative cooling is likely to be insignificant no matter what color it is. The water cooling system (if there is one) and air cooling (natural convection or forced airflow) are far more efficient cooling mechanisms. Even conduction through the engine mount may be more significant than radiative cooling.
And for that reason, shiny metal may be better than high emissivity paint. While bare metal has the lowest emissivity (and thus minimal radiative cooling), it has better conductivity, and therefore more efficient for air cooling. That’s why heat sinks on electronic components are often bare metal.
I was told by a fisherman that the reason many bottom fish are red is because it doesn’t reflect the infrared light that is the deepest penetrating light and so makes them effectively “black” in their natural environment.
That’s possible, but it isn’t something inherent to red. It might just be that they evolved a biological pigment with a very high infrared albedo, and that the pigment they evolved just happened to be reddish to visible light.
It seems a bit fishy, though (pardon the expression). If they’re worried about being seen by light penetrating from the surface, then it’d probably be near infrared that’s the biggest concern, and near infrared is right next to red. One would expect that a substance which is exemplary at absorbing near infrared would probably also be pretty good at absorbing red, and thus would appear either bluish or black, or anything at all except for red.