How hot is the surface of the Sun, in degrees Fahrenheit?

How to get close to this number

The colour is the clue. Stars are classified by temperature and the Sun sits in the yellow-white middle of that range — hotter than the red stars, cooler than the blue ones. If you remember roughly where the boundary between red heat and white heat falls for a glowing object, you have the order of magnitude, and the conversion between the two temperature scales does the rest.

The usual error is thinking of the Sun as a fire. It is not burning in the chemical sense; nothing in a flame comes remotely close to this, and no ordinary combustion could. The energy comes from fusion in the core, and the surface is simply the layer where the gas finally becomes transparent enough for light to escape — which is why the figure describes a boundary rather than a solid thing.

The strangest part is in the explanation and deserves repeating: the thin corona far above the surface is hundreds of times hotter than the surface itself. Heat flowing outward from a hot core should produce the opposite, and reconciling that is still an open problem in solar physics. Whenever a figure seems to run the wrong way, that is usually the most interesting thing about it rather than a mistake in the data.