Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

For the bonus riddle, I would say that the 'hotness' of the star is defined by the quantity of energy it gives away, which can be measured if you know the spectrum (E = hv), but in the same time, we need to compensate for the redshift (due to the universe expansion), and I think I read that it is possible, but I'm not sure how (except if you know the velocity of the star, or if you know the composition of the star, you can find from the absorption rays in the spectrum and deduce how much is the redshift).