My area of specialty is the corona, which is the outermost part of the Sun's atmosphere, so I'll answer about that.
The corona is very hot, in fact millions of degrees! The temperature of any given part of the corona will change a little over time depending on how magnetically complex that area is. If the area is quiet (meaning little magnetic complexity and no flaring) then the temperature will be 1 or 2 million degrees. If it's part of an active region (where flares come from) it could be 4 or 5 million degrees. It can get even hotter during solar flares, up to 20 or 30 million degrees (or maybe even hotter), but only in the vicinity of the flare.
A great mystery is why the corona is so hot, since it's much hotter than the photosphere (the surface of the Sun). We are still working to answer this question!
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