What the limitation or drawback to a stellar classification scheme based only on temperature?

Answer 1

One dimensional classification schemes are useful for sorting, but may not adequately describe the objects. In the case of stars, a temperature-only classification might assign the same label to a white dwarf, a main-sequence star, and a supergiant. In actual practice, stars are classified by a spectral class (corresponding to temperature), luminosity, and metallicity, with some additional tags for special cases. The simplified classification system is the Hertzsprung-Russel diagram, which maps spectral class (or temperature, or color) against luminosity.