Aurora image courtesy of Jan Curtis

They don't.

Actually the colors you see which look like SOMETHING ought to be red hot or blue-hot (or green-hot in the picture above!) does not come from the same physical process that makes iron bars glow red hot and white hot. What is happening is that individual atoms of nitrogen and oxygen are stimulated to emit light (usually green, but sometimes red) at only a few specific frequencies after getting kicked by charged particles raining down upon the upper atmosphere from the plasma clouds orbiting the Earth. The atoms emit the light, and it falls in parts of the optical spectrum we see as red or green.

The gas itself is no hotter than the other gases you will find in the upper stratosphere, which is usually around 300 to 1000 K. However, the currents flowing into the atmosphere to excite the aurora can heat the upper atmosphere considerably.

Aurora do not give-off heat to make themselves glow. They glow by the same mechanism as the gases in a typical fluorescent bulb and this is not a 'thermal' process that produces heat.

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