Currently, the Phoenix is bugged where you can tame it without super heat. Simply go to exactly where its ashes landed after it despawned, and spray the area with a wyvern/flamethrower, or throw down oil jars and light them. It will eventually tame. Its animation will be stuck, but uploading and downloading it will fix this.
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
This Might Take you a day or so but how I got my pheonix was i would look everywhere for a pheonix during a heatwave and you have to wait for the next heatwave to start this when you see the pheonix follow it and when it goes to the ground build a trap above where it despawned and when another heatwave starts it will be trapped: REQUIRED JERBOA AND FIRE WYVERN
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:)