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Does the color of an object affect its temperature?

This depends on what you mean by color. Some objects, such as stars or metals, will change color as they increase in temperature, indicating that they're radiating different energies. However, if you mean the "real" color of something, such as a plant or a shirt, then yes, there is a direct effect on temperature based on the color of the object.


The most clear connection between temperature and color will be based on interaction with...

This depends on what you mean by color. Some objects, such as stars or metals, will change color as they increase in temperature, indicating that they're radiating different energies. However, if you mean the "real" color of something, such as a plant or a shirt, then yes, there is a direct effect on temperature based on the color of the object.


The most clear connection between temperature and color will be based on interaction with light, as opposed to other methods of heat conduction such as convection. When light shines on an object, there are two possible effects; the object can either absorb the light, or reflect it. The color of the object corresponds to the wavelengths of light which that object reflects; oddly, when we say that something "is" this or that color, it's actually kind of the opposite. 


Many objects absorb or reflect multiple different wavelengths, so it's not easy to say that red objects, which represent lower-energy reflections, are going to be absorbing higher energies and therefore be hotter, or that blue objects will be cooler. However, in general, this trend is observed. The more high-energy (green, blue, violet) wavelengths the object reflects, the less energy it absorbs, and vice versa. 


On the other hand, we also need to take into account the intensity of the light being absorbed; if the object reflects high-energy wavelengths, but the source is primarily composed of red photons, then it may actually end up warmer than we expect. 

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