You could plant them now but it would be better to wait until they are going dormant and the foliage will be cut back. To plant them will require root disturbance leading to wilting and weakening of the plant,not a good thing in the heat of the summer.
You can during this time, build your soil by digging in compost which is all your clay based soil should need. I never find peonies to need chemical fertilizer when my clay loam soil is regularly composted. Peonies are not a drought tolerant plant and will do best with soil moisture malntained. Al

Thanks Al. So if I wait until fall, what do I do with them in the meantime? Just keep them in the pots? In the sun? In the shade? Thanks for your help!

Yes keep them in mostly shade, nursery pots can get very hot in the sun. Watch that the soil does not get too dry. If you feel they need any fertilizer stay away from any high nitrogen formulas. Al.

Anything that has been growing in a pot can be transplanted almost anytime (although some time periods would obviously be better than others). I say get that potted plant in the ground, disturbing the rootball as little as possible. It is very important that the peony "eyes" be planted close to the soil line--actually sticking up a bit above the soil line--or you won't get many blooms in the future.

Dig a big hole 1.5 to 2 ft deep and wide, and mix in a shovelful or two of compost into the loose dirt. Unless there is something truly awful about your soil, don't worry too much about it. A handful of bonemeal near the bottom wouldn't hurt, but isn't necessary. Refill the hole about 3/4s the way up and then get your hose and flood it until you have a little pond there. As long as that water soaks down in at least--oh, let's say--30-40 minutes (or less, 10 minutes perhaps)--you don't have drainage problems. If it still is a little pond several hours later or the next day, you have serious drainage problems. You'll have to re-dig the hole (when it dries out a bit) and mix in more good soil. (In most cases, you won't have that problem, however.) Once it drain well at the 3/4s level, fill in some more dirt and water well again (and make sure it drains well). What you're really trying to do is get that soil to sink down BEFORE you plant the peony--that way the peony eyes won't get pulled down too deep for blooming. Now put in your peony (rootball undisturbed if possible) so that the soil line of the plant sets up a bit above the soil line in the garden. Fill in the rest of the dirt and water again. This time, the watering should pull down the peony plant just a bit and it will be setting just right for the next 35 years.

Morning sun should be all right for the plant, but since hot weather may be approaching soon, I'd put a lawn chair over the plant for most of the hot days or rig up some kind of shade device to protect it from the hot sun. After the first year, you won't have to do that again.

Oh yes--make sure you are planting it in the sun. Peonies are sun-lovers.

That's what I would do--but it is your choice. You're kind of taking a chance either way--planting it now or trying to keep it healthy and thriving all summer in a pot.

Next time buy your peonies in the fall and plant them then. It will go much better and be a lot better for the peony. What you have going for you is that peonies are survivors!

Kate