Surface Temperature
It is important to know the star's temperature for many reasons:
The surface temperature of the star determines the temperature of the
radiation we see from the star (because this is where the radiation is
emitted into space).
The temperature of the star can be used to find either its Luminosity (if we know its radius) or its radius (if we know its Luminosity).
The temperature of the star is needed in order to place the star on an HR diagram. This allows us to estimate the stage of evolution of the star.
Astronomers have discovered that the surface temperatures of most
stars range between 2,000 K and 40,000 K. Our Sun is in the lower
part of this range, with a surface temperature of about 5,800 K.