Fire rainbows, illustrated in the photo by “Dehk” above, are actually not rainbows at all, but a halo phenomenon related to the sun dogs previously discussed.
Fire rainbows (or, more accurately, fragments of circumhorizontal arcs) are formed at an angle of 46° from the Sun, and result from light refracting through ice crystals in high-altitude cirrus clouds. In particular, they result from light refracting through one of the 90° angles of an ice crystal, like so:
Fire rainbows are on my bucket list too, given the many beautiful pictures of the phenomenon on Flickr and on Wikimedia Commons.
Scientific Gems 