Black Body in empty space Let's say we have a body of spherical shape with a temperature T > 0 Kelvin for our purposes.
It's supposedly in empty space. Completely empty space, no other radiation, no far away stars nothing.
So this body will be radiating EM waves of some wavelength related to it's temperature with most of the around a wavelength $\lambda_{max}$ as given by Planks radiation formula.
Will this Black Body at some point reach a temperature of absolute 0 ?
Does it depend on what material it is composed off which the minimum temperature will be reached?
 A: Temperature is related to the kinetic energy of molecules, atoms and subatomic particles of a medium or body. In a profound consideration, the motion - or more precisely - the acceleration of particles is accompanied by the emission and absorption of photons. These energy quanta are involved in every change of direction of the particles in a body.
In your case, a body somehow has a temperature in an otherwise empty space. There are no other bodies radiating and therefore a temperature increase of your body is impossible.
Your body has an outer surface. The surrounding empty space is the only condition for photons to escape from your body. Once emitted towards the empty space, the photon is lost to the body.
In the end nothing can stop the dissipation of energy (photons) inside the body. The cooler surface area (which emits photons and becomes cooler) is fed by the inner area. A condition to stop this process is unknown. Cooling down to zero Kelvin is unavoidable.
A: No, the black body are not going to lose whole energy because energy is quantized. The lowest level of energy will stay anyway.
$$E_n=\hbar\omega \left( n+\frac{1}{2}\right) $$
