This is a followup to a question about why the Falcon 9 second stage flame was invisible when out of the atmosphere. See: Why is the flame of the Falcon 9's 2nd stage invisible?.
That was well answered, relative to the fireball one sees at lift-off. However, it raised the secondary question of why the extremely hot gas and/or plasma of large rocket engines is not brightly glowing in the visible spectrum, whether in a vacuum or not?
Specifically, the temperatures of large space-capable rocket engines are said to be up to ~3500K. Why is it not glowing brightly with yellow to warm-white coloring just below the nozzle here?