How is the temperature of the Sun’s surface measured through its much hotter atmosphere, the corona?

The density of the plasma in the Sun’s atmosphere falls off precipitously as we move outward from the photosphere (its visible surface) to the corona. Because of this, the light we receive from the Sun overwhelmingly comes from its photosphere; only a tiny fraction comes from its corona. This is also why the corona can be seen only when the light from the photosphere is blocked (via a total eclipse or an occulting disk in a coronagraph). In fact, the photosphere is often referred to as the “surface” of the Sun, even though there is no real solid surface.

The color of light a star emits is related to its temperature. This means that we can determine the effective temperature of the Sun by measuring the amount of light it emits at each wavelength and comparing the resulting spectrum we see to models. Another approach is to record which absorption lines are present in the solar spectrum and determine their strengths; both the elements present and their strengths are sensitive to temperature. These different methods all show that the effective temperature of the Sun’s surface is around 5,800 kelvins (9,980 degrees Fahrenheit [5,520 degrees Celsius]).

So although the Sun’s corona at a temperature of over a million kelvins (1,800,000 F [1,000,000 C]) is significantly hotter than the photosphere, the vast majority of the light we use to measure the effective temperature of the Sun comes from its photosphere. The contribution from the corona is minuscule in comparison.