Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

From what I learnt in my physics class, the last riddle can be answered by Wiens Law, I think . I haven't learnt Rayleigh Jeans law (though it can be used) which applies accurately for long wavelength radiation unlike Wienns which is for shorter wavelengths.
Wiens law from what I understand stayes that the product between absolute temperature of the surface of a black body and the wavelength of maximum intensity emitted from that black body is a constant. So I think if you see a red coloured star its temperature at surface is higher than a blue coloured star. But thats assuming they rotate at the same direction at the same angular velocity cuz according to doppler effect they could actually be emitting mainly radiation of  the same wavelength but appear as different wavelengths(eg red and blue colours)...
I'm pretty sure I'm missing something so guys can you help out any mistakes I made?
Also Im assuming we're considering stars we can see(ie- visible light spectrum)