Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

Well, about the bonus question, if we say that a star can be considered a black body, the Stefan - Boltzmann law states that the intensity I of that star is proportional to its temperature T in the 4th power. So, if we can compare the intensities of two stars, either by using an instrument or by using a method that involves knowing the distances of the two stars from our point of observation, we can then determine their difference in temperature