Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

I think maybe the end riddle is not possible. I did something similar to this in my physics class, where we decided what substances were in a solution based on what light they emit when burnt. So, with what I learned from that, it could be possible, but not always. You could measure the spectrum of light a star emits, but it might not always tell you the tempurate of the star. This is because, for example, a star might be really hot and be made mostly of helium, while another star might be really cold(for a star) and have mostly oxygen, but they could emit the same spectrum of light, even though they're two different tempuratures. 
Although, I feel like this riddle should have a definate, "yes" or "no" answer.