Boomer

Blackbody radiation of visible light or infrared are the same.

If you use a white gas stove which has a lot of red content to the flame, a measureable increase does come with black paint - over 5%, I have data, but with very blue flames (propane/butane) it is difficult to demonstrate a measureable increase. I do have some pans painted black with whats called "header paint" for hot rods. Its a nasty process. My one winter pan with the MSR heat echanger is painted black. I used it to collect the data on my XGK.

Many people believe blackened pans is a myth - perhaps they never took physics, but in all fairness its difficult to measure and matters little, however as has been pointed out, a good windscreen with about a 1/2" gap all around helps. I have not been able to measure any increase from insulating the top of the pan ( which many people swear to) as the temperature of boiling water is not really high enough to cause much radiation ( as opposed to the flame temp), though I suppose it might save some energy from heat loss through convection, especially if you have a low heat output stove.

A windscreen is about all that matters, that and a lid to prevent cold air blowing over the pot from carrying away heat, however again before the water boils, not much heat is lost through evaporation, and when its boiling (and might matter)its done anyway. Without a windscreen it doesn't matter much what you do.

I have to add that my data was taken on stainless steel pots. I think there is an infrared reflection situation that makes the difference. Thin Titanium pots appear to pass heat like a glass pan - little or not relected heat - from them, so why bother to paint them. Also if the pan goes dry, toxic fumes are given off.

Comon - bring it on.
Jim