A group of Scandinavian researchers led by Göran Scharmer of Stockholm University have uncovered some clues about how sunspots stay warm.
Sunspots appear as dark blotches on the Sun's surface, and they represent spots where the Sun's surface is slightly cooler than elsewhere. Most of the Sun's surface is heated by convection currents which carry heat from the solar core, where nuclear fusion reactions that convert hydrogen into helium provide the energy that keeps the sun shining, up to the photosphere that we see. Sunspots form when the Sun's strong magnetic field is orientated to oppose these convection currents, causing the photosphere to quickly cool down, because there's nothing to replenish the energy that it's radiating away. Typically, it drops from its normal temperature of around 6000°C down to around 3000-4500°C.
But even at 3000°C, sunspots glow red hot, and without some heat source to replenish the energy that is radiated away, we would expect them to cool further. So why don't they? Writing in the journal Science, Scharmer and his colleagues present evidence that sunspots aren't regions where convection is completely turned off, but rather regions where it's severely weakened, so that some energy from the Sun's depths can still rise through to the surface.
Convection is normally recognised by the characteristic patterns of rising and sinking currents that it creates on the surface of the Sun, called convection cells. You can create a similar effect by looking at the pattern created in a pan of boiling water when you pour peas into it. But sunspots don't show these patterns, which is why they've long been thought to be entirely free of convection.
Scharmer used a different technique, effectively managing to look beneath the Sun's surface by observing it at a very specific wavelength, corresponding to a spectral line of neutral carbon which is only produced by material at temperatures of tens of thousands of °C. The Sun's surface is too cool to produce this spectral line, and so if you see it, it must be coming from deep beneath the surface.
Scharmer not only managed to detect this neutral carbon line at the edge of a sunspot, but also found that it had a blueshift, indicating that it was moving towards us, rising up through the Sun, at a speed of nearly a kilometre per second. That's the first evidence that has ever been found that there is still some weak convection going on beneath the surface of sunspots.