Hi Amy. Welcome to the forum! You can transplant potted Peonies, regardless of variety, pretty much any time. If the soil it's in is poor you'll want to remove it though so you'll do some damage to the roots. Tree Peonies should be planted much deeper than herbaceous as most are grafted to herbaceous roots, keeps the herbaceous growth from sprouting. An alternative would be to keep it in the pot for a few more months but keep it in a shady spot, your problem is probably just as much the roots getting too hot as the soil. Even if you decide to plant it out now I'd give it more shade for a few weeks to give it Recovery time