Color is usually associated with absorption of radiant energy. White reflects more radiant energy than black does, thus, a black object will absorb more heat than a white object will, given that all other conditions are equal. In the case of a coffee cup, the surface area and temperature differential are so small that the color makes no sensible difference. There may be a tiny measurable difference, but practically speaking, there is no useful difference. Use of a white coffee cup will at least encourage keeping it clean.
