Final answer:
The hottest stars are classified as O-type stars, which are significantly hotter than our G-type Sun, and M-type stars are among the coolest.
Step-by-step explanation:
According to today's classification of stars, the hottest of stars would be classified as a O-type star. Stars are classified into spectral classes based on their temperatures, utilizing the characteristics of their spectra. The spectral classes include O, B, A, F, G, K, M, L, T, and Y.
The spectral type O main-sequence star is the most massive on the main sequence, and hence most luminous and possesses the highest surface temperatures compared to other types of stars. Conversely, stars belonging to the spectral type M, also known as M-type stars, are among the coolest.
The Sun, which is a G-type star, has a surface temperature of about 5800 K, making it cooler than a type O star but hotter than a type M star.
The hottest type O stars can be over tens of thousands of Kelvin in temperature, which is several times hotter than the surface temperature of the Sun. The coolest type M stars can have surface temperatures as low as 2,400 K or even cooler.