For instance, could a star be hot enough to pass blue and become purple or green? If it is impossible for something to get that hot without exploding or imploding, are there theories as to which colors they would reach if they could?
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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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