As the point of this thread, trees grow outside. Delonix regia, I assume is the species to which you are referring, is native to Madagascar, with a temperature range from about 50° Fahrenheit to over 100°. Temperature shouldn't be too big an issue, as long as you introduce it to high temps and direct sunlight gradually. A bigger challenge in your desert climate will be keeping your tree in high enough humidity, as it comes from an area with over 40% humidity year-round. For us, that's extremely muggy, but for this species, it's a day at the spa.
You will probably get better advice from veterans here, but I would suggest moving into outdoor shade for about a week, then into partial sunlight for a week, then a little more sun, so that after 6 weeks or so it is in full sun.
You will need to be careful with your watering. It appears that it's cup may not have any drain holes, so you probably need to poke some in the bottom. Also, if you have some kind of shallow tray or dish to put underneath, you can keep it full of water to increase humidity in the immediate area of the seedling.
What kind of soil is it planted in