Light emitted by an object according to its temperature According to this picture

the light emitted by an object depends on its temperature.
That makes perfect sense when we heat a metal. As its temperature raises we see it red at first, then orange, then yellow... and then?
If we heated it even more should we see the metal turning green? and then blue?
 A: To see the green color, you have to use a green glass (a filter). The higher temperature, the brighter the green light emission.
A: You would be unlikely to see green. The problem is that in order to see green, you would need the spectrum of emitted light to peak at green and have relatively little contribution from other frequencies. This, for example, is the reason you do not see green stars (There is a cute Feynman story about this). An explanation of color temperature is given on wikipedia. Here is the path a black body takes with temperature increase--a Planckian locus diagram
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A: The phenomenon you're referring to is black body radiation. When a material gets hot, its electrons are in excited states. Occasionally, an electron will drop down to a lower state, emitting a photon. The higher the temperature, the higher the frequency of emitted light. 
This is why the heating element in your oven turns red. It's also how incandescent light bulbs work. Most of the light we see from stars is due to black body radiation, and we can infer the temperature of a star by its color because of this.
The equation that gives energy emitted as a function of frequency and temperature is Plank's Law. 

A: I'll show you an interactive diagram which lets you vary the temperature of a blackbody and see its effect on the radiated wavelengths.
But before you go there, recall that the visible spectrum is within the range of about $0.4$ - $0.8$ $\mu m$.
Here's the page with the diagram. As you increase the temperature, you'll find that the emitted radiation peaks over the range of wavelengths of visible light. So you're correct that the blackbody emits virtually the entire rainbow at very high temperatures.
A: Well its Violet, Blue, Indigo and Green ... So green by itself is a limited part of the band, and yeah just like how the others have explained about the contribution due to the entire spectrum, it would be hard to find out green amongst them. 
Blue-white would probably be more prominent as higher temperatures are achieved. 
