Does such a heavenly body exist called a black dwarf? It would be a Brown dwarf that has cooled to the point it no longer gives off heat or light.
A black dwarf is a white dwarf that has cooled to the point that it is no longer emitting light. However it takes a long time for a white dwarf to cool down. The exact timescale is rather uncertain, but at least hundreds of billions of years, perhaps hundreds of trillions of years.
The upshot is that that no black dwarfs exist in the universe today. The Universe is only about 14 billion years old, so there hasn't been time for any black dwarfs to form.
The paper A Dying Universe: The Long Term Fate and Evolution of Astrophysical Objects discusses brown dwarfs, black dwarfs, and other objects that may exist in an aging universe.
A black dwarf might be defined as a cooled, compact object with a temperature and surface area that are small enough to make it invisible in the optical part of the spectrum, with most radiation emerging in the infrared. However, because there is always some radiation in the short wavelength Wien tail of a spectrum this definition would be distance-dependent, so instead you could define a temperature below which you could argue that so little light emerges at visible wavelengths that it would be dark. Again, this is somewhat distance-dependent, but also depends on the size of the object.
In practice, at astronomical distances, cool compact objects like old white dwarfs and neutron stars, or low-mass and older brown dwarfs are invisible at optical wavelengths when their temperatures fall significantly below 3000K. At 3000K, the V-K colour of such objects is $\sim 6$, meaning they are 25 times as bright in the near infrared. This increases to $\sim 100$ at a temperature of 2200K.
There are lots of brown dwarfs (particularly the T-dwarfs) that can only be seen in the infrared. The coldest known white dwarf is probably older than 10 billion years, has a temperature below 3000K, and has not been detected at optical (or IR) wavelengths (Kaplan et al. 2014).
There are likely about a billion or so old, cold neutron stars in the Milky Way that cannot be seen via electromagnetic radiation at all unless they interact with something else.
The Wikipedia definition of an object so cold it doesn't emit light is simply unworkable. All objects above absolute zero will emit electromagnetic radiation (light) and it is hard to see how an object could cool to below the cosmic radiation background.