If the tree is acclimated to the outside weather, I'd say go ahead. If it's been inside for a long time, then I'd acclimate it by putting it somewhere cooler while it's still getting a bit of light.

"If good horticultural practices are used, trees can be planted any time of the year. Container-grown trees suffer minimal root disturbance during transplanting. If they are carefully watered after planting, trees can be successfully planted even in midsummer.

Bare root trees are generally not available for planting except in their dormant condition, during late winter and early spring. However, research at MU has shown that bare root trees can survive summer planting in certain conditions. Bare root trees with up to 2 inches of stem caliper can be planted with excellent survival during the midsummer if preconditioned in a bed of irrigated pea gravel (called the Missouri Gravel Bed) for 10 to 12 weeks. If harvested and stored properly, B&B trees can also be planted at any time of the year.

However, since conditions during midsummer are often stressful to plants, most nursery professionals recommend planting in spring or fall."

Here is a link that might be useful: University of MIssouri Extension Tree Planting Guide Sheet

It would be safer outside than inside. If it is used to being inside, yes get it used to outside gradually.

We planted 1 bare root tree and two potted trees that Stark Bros shipped to us last week. I would think your tree would do fine. I would mulch it well but not close to the trunk keep it 3-4 inches away to discourage mice chewing the trunk.