Best to follow it, and watch it's ashes fall. Build a *5 high* trap with stone doorways. Make sure it has a roof. At the next super heat bring over a fire wyvern. Use rare flowers to lure it closer to your base just to make it easier.
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
It introduced a new taming method,while not the pseudo-boss we prayed 4 but to tame it u set it on fire with flame arrow,flame throweror a fire Wyvern,they only spawn during heat waves.keep this in mind.