Effects of inner painting in the temperature of room which room will stay warmer for long time in winter night. The room with inner painting black or white?
 A: It will make no measurable difference.
Heat in a room is lost by conduction and convection - not (in significant amounts) by radiation.
Radiative heat transport occurs between two objects at different temperatures, so the surface of the wall would have to be colder than the rest of the (objects in the) room for radiative transport to take place.
Assume a black sphere in the middle of the room at temperature $T_1$, and a wall at $T_2$. If the walls are "black" (maximum emissivity at the wavelengths of interest - note this is not just black in the visible since most thermal radiation is in the far IR) we can compute the rate of heat loss as
$$Q = \sigma(T_2^2-T_1^2)\pi r^2$$
For a wall at 0C and a sphere at 20 C, this results in heat transport of about 100 $\rm{W/m^2}$ from the object to the (perfectly black) walls. In reality there are not walls on all sides - so the solid angle is smaller and the rate of heat transport is less - and furthermore the walls are not that cold. Because if they were, there would be significant heat transport from the air. 
For this you can refer to this engineering toolbox link. With a very modest rate of air flow you will have a heat transfer of about 20 W per square meter per degree of temperature difference. This would quickly result in a heating up of the wall surface to "something close" to the temperature in the room - at which point the radiative losses are even smaller.
It may already be obvious from the above but let me spell it out: radiative cooling would (very slightly) affect objects in the room; but the air has very little radiative interaction.
At "normal" temperatures, and with a house that is somewhat insulated, you can ignore the radiation component. This is not necessarily true if you have a flimsy tent - you may have come across the aluminized Mylar "emergency blankets" that provide radiative insulation. They do make a difference when that's all there is between you and a cold dark clear sky. Not the same thing at all.
A: The scientific fact is that white reflects the radiant energy rays of the sun and black absorbs them.
Most major paint manufacturers can tell you the Light Reflectance Value (LRV) of any color paint chip. White reflects 80% of the light, black 5%.
So if you want to have a warmer room paint it black since more of the radiant energy of the light will be absorbed to keep the room warmer.
