Final answer:
Stars cooler than our Sun, which has a spectral type G2 and a temperature of 5800 K, would have spectral classes K, M, L, T, or Y, with M stars being up to 1.66 times cooler than our Sun. The temperature of the coolest M stars is below 3500 K.
Step-by-step explanation:
Stars are classified according to their spectral types, which reflect their surface temperatures. Our Sun, with a spectral type G2, has a surface temperature of approximately 5800 K. Stars are ordered by spectral classes O, B, A, F, G, K, M, L, T, and Y, from hottest to coolest. Since the student is asking for stars with a lower surface temperature than the Sun, we are looking for stars with spectral types later than G2. The classes K, M, L, T, and Y are all cooler than the Sun. Therefore, any star with one of these spectral classes would be cooler than the sun. The coolest M stars have temperatures below 3500 K. Comparing the temperatures, the coolest M stars are approximately 1.66 times cooler than our Sun (5800 K / 3500 K).
Regarding the part of the question about the hottest O stars, they have surface temperatures over 28,000 K. To find out how many times hotter an O star is than our Sun, you would divide the temperature of the O star by the Sun's temperature, which results in roughly 4.83 (28,000 K / 5800 K). However, this question specifically requested information on stars cooler than the Sun, not hotter.