Question: What is the boundary temperature where star does not emit visible light anymore?
What is the boundary temperature where star does not emit visible light anymore? I know that the hotter the star is the more its peak of spectrum is towards the ("left side") bluish color. For example the sun emits mainly yellow, because it's temperature is 5000 K.
I'm not sure why Big Daddy got two thumbs up for his answer considering it has absolutely nothing to do with your question. His link cites the Draper Point which is the temperature at which a blackbody begins to glow. It really has nothing to do with being a temperature of a star that does not emit visible light. In fact, no star could ever possibly be 798 Kelvin.
I think you are also not completely understanding how a star works. Stars are a type of object known as a blackbody. A blackbody is something which emits at all wavelengths. So you're essentially asking, "At what temperature does this object, which emits at all wavelengths, not emit at this particular wavelength?" It just doesn't make any sense.
However, in a blackbody, there is something known as the peak wavelength. That is the wavelength that the object emits most strongly at. And as you correctly stating, our sun emits most strongly in the yellow. And it is also true that as a star get's hotter, it's peak shifts more towards the blue.
From our observations, we know stars range in temperatures from about 2000 K at the coldest, to 50,000 K at the hottest. This means the peak wavelengths occur between 1500-50 nm (using Wein's Displacement Law). The visible spectrum is between the wavelengths of 700-400 nm. That means the coldest stars radiate in the Infrared most strongly, and the hottest stars radiate in the UV most strongly. However all of those stars, still radiate some easily measurable about in the Visible band.