For full Phoenix taming details, get the taming calculator app.
To tame a Phoenix, shoot it with a flame arrow, flamethrower or Fire Wyvern. Weapon quality impacts taming speed; a 200% damage bow will be twice as fast as a 100% bow. Please ignore taming effectiveness and taming times as the Phoenix has unique calculations. Have a good taming technique idea? Share a tip!
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:)