mirages only happen in extremely hot weather
This is not true. If you restrict your definition to only the shiney puddle-like image that appears on the ground at a distance, then the phenomenon only requires the ground to be hot enough to heat the air above it. Ironically, this is more prone to happen on a colder day with more direct sunshine.
There are also other phenomena that sometimes go by the name "mirage".
Under the right conditions one can see refracted images of harbor cities in the sky at night when the line of sight to the harbor is obstructed by the horizon.
Also, even in RE accepted theory in which the Sun sets, the light is refracted by the density gradient of the atmosphere (so similar to the mirage effect that the distinction is entirely academic) during sunrise and sunset so that you are able to see the image of the Sun even before and after your line of sight to the Sun has been occluded. This is the REer explanation for the squashed appearance of the Sun when it osculates the horizon.