As far as visible light (which can have color), the hottest color would very likely be white. Objects like a star, once it gets hot enough, it will radiate in all colors – a phenomenon called (perhaps confusingly) black body radiation.
It would be white with perhaps a bit more blue/violet. It would be so intense, though, that what we could “see” would be white. So, no, a star would not turn purple or green.
The more energy a photon has, the higher the frequency but beyond violet, it is no longer visible and therefore would not be termed a color (to be pedantic). Photon energy beyond visible, would be ultra-violet, x-rays and gamma rays in ascending order (at least the one’s we’ve given names).
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