That looks like one of those whistling past the graveyard kinds of things. The temperature jumps from about 5000 (cornea) to a million (corona), and based on physics models it shouldn't be doing that. If low density were a factor, there wouldn't be any data to support the observation of the anomaly.
As long as we agree that “heat” is the measurement of the movement of atoms and molecules, then we both probably agree that “density” matters.
For instance, if the temperature of the Earth's atmosphere was 1 million degrees, the Earth's surface would vaporize in a couple of minutes.
However, if the density of the Earth's 1 million degree atmosphere was reduced by 99.99%, it would probably take centuries for vaporization to occur, or maybe even never.
“Super-heating” in the corona is a really interesting puzzle, but I think most people imagine the corona in terms of the density of the Earth's atmosphere, which is not correct.