Phoenixes can spawn anywhere on the map during a heatwave and turn into a pile of ash when it ends. When the heatwave returns, it'll respawn wherever its ashes fell (usually right below where it was flying when the heatwave ended).
If you find a Phoenix (they fly VERY close to the ceiling), pay attention to where its ashes drop at the end of a heatwave and build a trap over it so next time the heatwave happens, the Phoenix spawns inside your trap.
I also recommend bringing a Fire Wyvern so when it respawns you can just torch it and not take any damage from its fireball.