If one wears a black shirt to sleep, would it keep you warmer that if it were white?
Kirchhoff's law says that for a certain wavelength the emissivity and absorbance are equal. If a shirt is black we know that its absorbance and emissivity are large in the visible spectrum, but the shirt emits radiation mostly in the infrared. So we can't really know the emissivity of the two shirts just by their color i.e. we cannot see how dark they are in the infrared.
Understand that the difference between a black and white shirt is that the black shirt has a greater absorbance and hence a greater emissivity(objects that absorb most also emit the most heat by radiation, as emissivity is equal to absorbance by Kirchhoff's laws). Thus if your room had a thermostat and the white shirt and the black shirt were the same temperature at the beginning, then if the room's temperature fluctuates etc. then the black shirt would lose heat faster then the white shirt(which has lower absorbance hence lower emissivity). Thus you would actually stay warmer in theory with the white shirt as it would lose heat more slowly after temperature fluctuations, in the dark.
Black objects can radiate energy (heat) as good as they can absorb it. If you wear black shirt while sleeping (i.e when there is not much light to absorb), the only thing your shirt would be doing is to radiate heat, which black objects do better than white objects. So, you would feel cooler.