Would wearing clothing that is black on the inside and white on the outside keep you cooler? The Straight Dope ran an explanation of why nomads often wear black clothing - it absorbs heat better from the body. On the other hand, white clothing reflects sunlight better. Is it possible to get the best of both worlds and wear clothing that is black on the inside and white on the outside?
 A: Direct sunlight falling on people walking in the desert calls for white or light colors.
The coolest sun shades are white, also sun umbrellas. Coolest clothing, black versus white,  is light colored. The reason is that in direct sunlight  the energy of the sun, could be 1200 watts/metersquare all falls on the cloth. White reflects the visible light, which is most energy from the sun, so much less is absorbed to reach   the shaded tables underneath .


Desert nomads of Cholistan in Punjab come to the annual festival at Channan Pir.  

As one can see the dominant dress is colored white. Black is the color of mourning and it might be that some women wear black even in the sun, and one will see light colored or brightly colored clothing occasionally due to the human tendency for decorating the self, but white is predominant. I checked on google and the statement in your link that Tuareg wear black is not correct. Most photos are white or light colors (similar arguments). Maybe they wear black for camouflage at night if on the war path?
Flowing robes also can be seen , no tight clothing, so that the air circulates and by convection cools the body as it perspires. 
So the question becomes: would a black ( black in the infrared, totaly absorbing infrared material ) lining inside a white robe help in cooling the body by removing infrared radiation faster? My guess is yes, but cannot guess how much faster. The infrared radiated from the body would be better absorbed and transmitted to the outside but the main mechanism would still be convection.
A: The color of a surface doesn't reliably indicate the emissivity at non-visible wavelengths.  The color in the visible spectrum is more of a side effect than anything.  Most thermal radiation around body temperature or room temperature happens in the infrared region, not the visible, and that's not reliably indicated by visible color:

(Source: JPL)
The visibly transparent glasses are opaque to the body's infrared emissions, while the visibly opaque trashbag is transparent to infrared.  So one property has no relation to the other.
The emissions of the sun occur mostly in the visible region, which is why white clothing reflects solar energy and stays cool while black clothing absorbs solar energy and gets hot:

(Source: User:Dragons flight)
But your body's thermal radiation is in the infrared, so this rule doesn't apply to the inside of clothing (unless your body is hot enough to radiate visible light, but then you have bigger problems).
Your basic idea would work, though, if you found a material that reflects visible light while transmitting infrared light (but that material would probably have the same properties on the inside and outside, and thus be visibly white on the inside, too).

For example, white paint is quoted as having an absorptivity of 0.16, while having an emissivity of 0.93. This is because the absorptivity is averaged with weighting for the solar spectrum, while the emissivity is weighted for the emission of the paint itself at normal ambient temperatures. ... The white paint will serve as a very good insulator against solar radiation, because it is very reflective of the solar radiation, and although it therefore emits poorly in the solar band, its temperature will be around room temperature, and it will emit whatever radiation it has absorbed in the infrared, where its emission coefficient is high. − Kirchhoff's law of thermal radiation

NASA uses such materials, which they call "selective surfaces", and are used to cool the Hubble telescope:

These surfaces can be designed to reflect solar radiation, while maximizing infrared emittance, yielding a cooling effect even in sunlight. On earth cooling to -50 °C below ambient has been achieved, but in space, outside of the atmosphere, theory using ideal materials has predicted a maximum cooling to 40 K!


Wikipedia's article on selective surfaces describes the opposite effect: Transmitting sunlight and blocking infrared from escaping, to capture the sun's energy.
A: Since both absorption and radiation depend on color in the same way, this would decrease the energy that is radiated off into the surroundings. So if radiation were the only way to lose heat color wouldn't matter, and in the long term you'd have the same temperature as the incoming light.
But since nomad's don't live in vacuum there are other ways of heat transportation. What color is best depends on which forms of energy transportation dominate.
Since I guess that you lose more heat to other sources than radiation, while a large part of the incoming heat comes from light, making them white on the outside and black on the inside could make sense. But there are complicating factors such as wind, vaporization of sweat,...
A: Since outside interacts with the radiation both ways, it would not help. But, there's something that would:
You need to have clothes which are Black (totally absorbing) in visible light and White in Thermal-infrared wavelengths (totally reflecting). This color is called Red (well, to some extent: if you shift the spectrum into visible terms).
A: If the temperature inside clothing is the same as outside, the wear will not do anything.
This is because white surface worse adsorbes light but also it worse emits infrared radiation. Conversely, dark surface better adsorbs, but also better emits.
In the case the outside temperature higher than inside, such wear will help to be cooler, but even better wear would be that one which has the both sides white. Similarly, if you want to keep heat in winter night, you would prefer the all-white wear because it better keeps the difference in the temperatures.
Conversely if you want your temperature to be as close to that of environment as possible, you should prefer all-black wear. 
A: theoretically yes. If the white garment on the outside is opaque enough, it will block more of the sun's light from reaching the inner black garment. The black garment will actually help you keep cooler if you have both garments made properly. This is because black does not actually absorb heat, it traps it therefore not allowing the "cooler" air to heat it up. Of course cold mixed with warm creates HOT as is with starting a fire, for instance. You'll notice in the summer time it's harder to start a fire than in the late fall.
People toss the word absorption around as if they know what they are talking about. Black doesn't ever absorb heat because it doesn't get as hot. It can but not for the same reasons. White will do the absorption but that's not something you need to worry about. You want the white to absorb the heat because that's the only way it can be reflected back out. Like a sponge that is filled with water, only to reflect the water with it's added weight and eventual slow purging. Of course liquid is slower than light, so that explains the time it takes for the sponge to become dry again (on it's own). You'll notice the lighter the color the less dense the material is - if it's not just the dye, of course. 
The reason you will probably die with a black garment on the outside while walking in 110 degree desert heat is because the heat the sun is shining on you doesn't seem to want to move anywhere except where it meets the garment. So the synergy of your body heat and the sun's heat being trapped create more heat. If you wear white on the outside however, it will do better to reflect most of the sun's rays, while the black garment on the inside provides you with further protection from reflection of the sun's rays getting through the white garment. That's why most power cables that run from the telephone pole to your house are coated in thick black rubber or composite material. Painting power cable rubber white will actually help protect the copper wiring from heat damage, that much is true. But the paint will just wear away and rubber is naturally black so... 
