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You’re right, yes the bright regions are typically hotter but more so are stronger in magnetic strength and represent areas where the internal magnetic field of the sun has popped outward of the sun’s surface resulting in these band-like structures which are actually just plasma moving in helical formation around the magnetic field lines (because plasma motion is dominated by magnetic forces) that reach out of and back into the sun’s surface.
What is magnetic about the sun? [The internal dynamo effect](https://en.wikipedia.org/wiki/Dynamo_theory) generated by very strong electrical currents in and around the core which then generate strong magnetic forces as a result. This can be studied more by looking at Maxwell’s equations if necessary.
This sun’s magnetic behavior goes in roughly 11 year cycles starting from a “solar minimum” or a period of almost no regions forming loops such as this, or if they do, they are very small, simple and typically at very high latitudes. Then, due to the fact that the sun is not a solid, but instead rotates at different rates, at different latitudes, begins to pull and twist magnetic field lines so that they become twisted and very complicated over time. This results in more regions, more often, and much closer to the equator. Currently we’re at our solar max (or what is currently predicted as a possible double peaked max and we are going into the second peak) so the year before was considered our first maximum.
That is why there are so many bright regions around the equator.
There are a little more complications than this, such as why magnetic field lines get twisted because of the differential rotation of the sun, and the distribution of that magnetic “flux” as we call it from solar minimum to solar max, but that is, for the most part, the gist.
Source: 4th year Astro-physics major specializing in Heliophysics.