Is heat needed to make a natural rainbow?

Sometimes, when you look at the sun or the moon, and there is high thin cirrostratus clouds, you can see a halo around it. Well, it is the same as a a rainbow, the light spectrum is displayed as each frequency reflects at a different angle on the ice crystals at the top of the troposphere where the temperatures is perhaps -40 (note that I don't say, Fahrenheit or Celsius because at -40, both scales meet and are the same! ;-)

Therefore I don't see why heat is needed to make a natural rainbow. When I fly, here in cold Norway, my little aircraft right above the clouds, in very cold weather, I can see a rainbow as a circle around the shadow of my aircraft on the cloud.

Incidentally, did you know that tiny water drops can be cooled down to -20 C before they turn into ice crystal? Yes, that is because, in order to freeze, water needs first to release latent heat energy and it can only do it when touching what we call a condensation nuclei such as a smoke particle, dust, salt crystal or pollen. Just anything with enough mass to absorb the energy.

humidity, because the light is being reflected off the water molecules in the air I would assume. Where there is humidity, there is heat, so I'd say yes.