Scientists learned the temperature of the surface of the Sun from looking at how the intensity of the sunlight varies with wavelength (color). The fact that the Sun looks yellow, rather than more white or even blue (as some stars do) already gives us a clue as to the temperature of the surface. The temperature under the surface was first studied by using computer models of the interior density and temperature of the gas and fitting these models to the observations. More recently, the temperatures in the outer layers of the Sun have been measured directly (confirming the models) using a techniques called "helioseismology" -- which measures the speed of sound waves at different depths in the Sun. From the sound speed, scientists can determine the temperature.