(from http://xkcd.com/54/, showing the spectrum of the cosmic microwave background radiation)
As a result, only some colors are possible: the ones that can be formed by a black-body radiator with this shape of spectrum. The line in the CIE diagram below shows the possible colors of black-body radiation, depending on the temperature:
You will see essentially the same colors from incandescent light bulbs and toaster heating elements as from a star -- a 2700K tungsten filament will radiate light that appears to the human eye with the color corresponding to 2700K on the above diagram.
The "black body" curve does not go through anything you could really call green.
Qualitatively, for something to appear green, it essentially needs to stimulate the medium-wavelength cones more than the long- and short-wavelength cones in the human eye. Black-body radiation is too broadband to do this.
Here, the colored lines represent the sensitivities of the three kinds of cones in the human eye. The dashed line is black-body radiation from a 5400K star, obeying Planck's law. Black-body radiation is way too broad to hit the "green" cones without also hitting the "red" and "blue" ones. That's why this light appears white.