Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

I'm assuming that by using the star's colour, you mean eyeballing using nothing more than a visible light telescope. In that case, as a star gets hotter, the frequency at which it emits the most energy moves toward the blue end of the spectrum, so the hottest stars would have a blue (or possibly even violet?) colour, while others would appear white/yellow/orange/red.
P.S. Any star (other than a supernova or similarly violent and brief event) close enough to see as an individual star rather than part of a galactic cloud is, in comparison to the observable universe, right next to you, so it won't be moving any significant fraction of the speed of light, and the Doppler effect shouldn't be noticeable.
If we are talking about measuring the temperature precisely, we can analyze the spectrum and compare where the absorption lines are to where they would be on a stationary light source, and this way measure and correct for any Doppler effect.