I have a black helmet. Originally I thought it could make my head too hot, but that hasn't been my experience.
Then I did some calculations.
The helmet has a surface area of maybe 0.15 square meters. That can in theory absorb 150 watts of heat. However, it's similar to a hemisphere (although the radius is different in different directions), so considering that sun shines only from a certain angle, it's more like 0.05 square meters or 50 watts of heat.
The cushioning is made from 2.5 cm thick expanded polystyrene. Expanded polystyrene has heat conductivity of 0.04 W/(m*K)
So if we assume the surface gets so hot it's enough to boil water, and your head is 37 degrees Celsius, it's 63 K * 0.15 m2 * 0.04 W/(m*K) / 0.025 m = 15 watts of heat transferred to your head. However, I have never been able to boil water using my black helmet so clearly the assumption of 100 degrees Celsius temperature at the helmet surface is incorrect.
And here's why it can't boil water. The 50 watts of heat it absorbs is carried away by the wind. The frontal cross section is 0.05 m2, so at 25 km/h or 6.94 m/s, 0.347 m3 of air pass over it every second. That's about 0.42 kg of air every second. The venting holes are made such that most of the air goes via these, some of the air can flow over the surface of the helmet. Air has a heat capacity of 1000 J/(kg*K) at constant pressure so every second, 420 Joules of heat is extracted per Kelvin of temperature difference.
So to extract 50 watts (50 Joules per second), we need 0.12 Kelvins of temperature difference.
So now we know how hot the helmet exterior is. It's 0.12 Kelvins hotter than your head, not enough to boil water. So 0.028 watts of heat gets conducted to your head via the polystyrene.
If you produce 150 watts of power at 25% efficiency, that's 450 watts of discarded heat. Head surface area of a non-obese adult is 9% of the total body surface area, so if we assume that each body part is proportionally doing its share to discard waste heat, your head is discarding waste heat at a rate of 40.5 watts.
So 0.028 watts / 40.5 watts = 0.07% approximately.
A black helmet in full sunshine therefore makes your head 0.07% hotter than it would be barely from riding the bike.
And remember here you are considering, not a helmet (which can be either black or white), but a visor. A visor doesn't even touch your head, it's just something over your eyes.
I would select a black visor. Black absorbs sunlight, white reflects sunlight albeit in a mostly diffuse manner and not specularly. Therefore, black would be best for your vision.
As for helmet, if I had a choice, I would select a bright green helmet because it's the most visible in traffic. However, my helmet selection criteria are (1) Snell certification, (2) in-mold technology, (3) MIPS, and looking at the current Snell certified helmets list makes me really sad. Out of general-purpose helmets, Specialized was the only company certifying its helmets to Snell standards. It has abandoned the Snell standard. So every Specialized helmet that's a recent design has a high chance of not meeting the Snell standards. Therefore, it looks like I can no longer purchase reasonable helmets.