This creature will not respawn in the same location after superheat. Be mindful of this. Best way is to have a search party looking for it if you can. I'm not sure if this is the case for admin-spawned Phoenix's but I waited next to where the ashes of a Phoenix were despawned on a server and on the next superheat, there was no Phoenix there or at all in that area. Ensure your fire wyvern has plenty of stamina or you will be landing far too often to tame it.
You can get it to spawn next to your base because of the following: It always respawns at it's last location, so if the heatwave ends while you are following it you will know where it is for the next heatwave. It also chases you when you eat flowers... hint hint
Find a phenix during a heatwave and follow it until it ends. The phenix will turn into ashes and land on the ground but will spawn right back at the same exact spot during the next heatwave. Build a trap 6 blocks high so I can't glitch out and you have yourself a trapped phenix to tame:)
Fun fact! You can tame the Phoenix by hitting it with a torch so you don’t have to waste you’re time shooting it and missing and what not just wanted to help everyone out because this creature is definitely something worth getting