Basically the above. Building a great fire and the thought came up.
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Because the combustion produces particles in the flame that are warm enough to emit visible light.
All object warmer than absolute zero emits thermal radiation. The amount and frequency spectrum depends on the temperate. We can see the infrared light our own bodies emit but we have instruments taht cant, they are usually called thermal cameras.
When the object reaches a temperature of around 480 °C (896 °F) we star to see a faint red glow. Even if an object gets a lot warmer the still will emit visible light. https://en.wikipedia.org/wiki/Thermal_radiation#Subjective_color_to_the_eye_of_a_black_body_thermal_radiator
The arc produced in welding can be warmer than the surface of the sun, They will contain UV light that can damage you eyes so you should not look at to warm objects
You can detect thermal radiation when IR light hir your skin its heat is up and you can feel that even if objects do not emit visible light. That it is not just warm air you feel is easy to show. But something in-between like a sheet of tinfoil that reflect the radiation. As soon as it is removed you can feel the heat. Hot air does not move that fast.
It is not just as simple as temperature. Gases are very bad at absorbing light taht is why we can see through the atmosphere. It also means they are bad at emitting light so even if they are warm they are quite hard to see. What you see in a wood fire is glowing hot solid carbon. If the wood does not burn up you can clearly see the black carbon that remains, it absorbed light very well which is why it is black. That also mean is is very good at emitting light when it is warm. In the smoke, it is soot particles of carbon that you see.
This explains why some flames for example flames from burning methanol are very hard to see, they contain very little soot and can be practical invisible.
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