Why do sunspots stay cooler than their surroundings?
Sunspots are areas on the surface of the sun where strong magnetic fields keep charged particles trapped. Matter on the surface convects (gets heated, rises to the surface, cools, and sinks down only to be reheated and continue the cycle) but not the matter trapped in these magnetic fields. It can't sink back down once it cools off, which is why it looks black from Earth. These spots are still 3000 degrees kelvin (essentially Celsius) which is really hot but colder than the surrounding 5800 kelvin surface.
C Convection currents arise to the surface cooling the plasma underneath