76.45% of main sequence stars are classified as M-type. So median temperature is much lower than the sun. If you list the brightest visible stars then the sun is closer to median. The milky way looks redder than the zodiacal light. That is not a precise number but you can collect the ballpark data yourself on a clear night using no equipment (if you can get away from city lights). Most astronomers use the star as a point source. For far away stars it is impossible to separate the corona and photosphere except during eclipses. The temperature is determined by the spectrum. A star's spectrum is compared to radiation from a black body. Core temperatures in red giants are much higher than core temperatures in similar mass main sequence stars. Red giants are considered cooler stars. The classification is entirely based on the light that is observed.