Why is a light colored T-shirt cooler to wear than a dark colored T-shirt?

Sunlight consists of a mixture of all visible wavelengths of electromagnetic radiation (light). When all visible wavelengths enter the eye simultaneously, the color white is perceived. Black is the absence of any light. Other colors are sensed when selected wavelengths are present--longer wavelengths are perceived as red, shorter ones as blue or violet. 

An object's color in the sun depends on which wavelengths it absorbs and, therefore, which are reflected away from the object. A shirt that appears red absorbs the shorter wavelengths and reflects longer ones. The reverse is true for a blue shirt. So while a white, or lighter colored, shirt REFLECTS most of the visible wavelengths it is exposed to, a black or dark shirt ABSORBS more wavelengths. Absorbed radiation is converted into heat, making the darker shirt warmer to wear.

Source: www.physlink.com/Education/AskExperts/ae80.cfm