When sunlight falls on an object, one of three things can happen: the light can be reflected back to where it came from, the light can be transmitted through the object, or the light can be absorbed. When light is absorbed, the object will heat up. Now black paper absorbs most light, whereas white paper reflects some of the incident radiation (light). Hence, black heats up more than white.

We should be very careful with how to phrase this question. White paper does not actually get cool when it's exposed to the sun! It still gets warm, just not AS warm as black paper does. Black paper gets warmer than white paper when exposed to sunlight because black absorbs more radiation (in the form of heat and light energy) from the sun. White paper, on the other hand, reflects more of the heat and light energy.

Light is energy, as is heat. Dark colors absorb light, while light colors bounce it away. This means that something dark will soak up light and become hot when light shines on it, while something light will remain cool.

Have you tried doing an experiment to see if you can reproduce this effect? Also, I don't know if the white paper would get cool, or just that it wouldn't get as hot as black paper. Although I'm not sure how significant the difference would be, my guess is that, on average when compared to black paper, white paper reflects more light, so it absorbs less energy from visible and near-visible light. Because it absorbs less energy, it doesn't get as hot.

Heat and light are both different types of energy. Light energy can be converted into heat energy. The black paper absorbs all of the sunlight and converts it into heat, so the paper gets warm. The white paper reflects almost all of the sunlight, so the light is not converted into heat and the temperature of the paper does not increase noticeably. What happens if you put colored paper in the sun? It should get warmer, but not as warm as the black paper, because it is only absorbing some of the colors of light and converting them to heat!