I have successfully grown peonies in hot, dry Pasadena - even the herbaceous peonies that are so popular!
I'll share some tips but first, some general information to help you better understand peonies: There are three main types of peonies, Tree peonies that grow continuously (sounds scrumptious, not sure I've ever seen one in person), herbaceous peonies that die back at the end of the season, and Itoh peonies that are a hybrid between the two. Tree peonies have a greater heat tolerance and apparently get quite large. Herbaceous peonies need something to cause dormancy so they can rest and set buds. If you don't have chill then a dry dormancy *can* initiate bud formation (though it's far less ideal than having a cold winter do it for you). Peonies generally get listed as good for up to zone 8. Pasadena is solidly in zone 10. Because we are on the weird west coast (at least according to the general horticultural wisdom) we can get away with zone 9 plants fairly easily (my hellebores area testament to that) but zone 8 is pushing it. I make sure to plant peonies where they are sheltered from afternoon sun and always aim (though space issues don't always make it possible) to put them in a spot that gets a few hours of morning sun or at least part sun. Then it's all about patience. Disbud those plants for the first 2 years. By the third year, if they are going to bloom, they ought to HOWEVER maybe not here in our hot climate.
So here I am telling you that YES YOU CAN! and your next question should be "But should I?" The answer to that is a bit more complicated. I have a deep love for peonies and a real tendency for pushing the horticultural edge. Peonies don't take up a lot of space per plant but there are things you could plant in their place that would be much more rewarding. If you want lots of flowers, plant a rose bush! They are incredibly happy in our hot and dry climate! If peonies have your heart, then listen carefully. Some put ice on their plants in the winter to mimic chill. I don't advise that. First, it's a waste of energy. Second, a plant that needs that much maintenance is very likely to fail as you will get busy and forget. Third, how much ice? How often? Without some clear guidelines it's a crap shoot (and a waste of time and energy). Don't expect miracles. This year was we had a wonderfully cool winter and a lot of rain. I have more peony blooms than I've had in years past. When it hits 80 degrees for a spell they will probably be done but I'm crossing my fingers for a couple more Itoh peonies to bloom. This is a many year investment. These plants can potentially live for longer than you (though not likely in this climate). Don't count on having blooms every year. After four or five years, once plants are well established then you'll have a better idea about how they perform. WHO HAS THE PATIENCE FOR THAT?! You have to be a real nut to do this. If you don't already know this then prepare for some serious sticker shock when you go shop for roots. New and highly desired peonies can run more than $300. Even less desirable ones are likely to be at least $20 (and those might not even be worth it to try and grow here). Peonies are EXPENSIVE. And not guaranteed to succeed. Did I mention this is a bit of a fool's errand?
Now, if you are still reading and still want to try, don't say I didn't warn you. Here are my tips for success (keep in mind that's really "success"):
Location: Choose a spot that gets zero afternoon sun and is sheltered from the extreme heat of afternoons. If you have a frost pocket in your yard (plant nasturtiums in January and see which ones die from cold - sometimes you can identify this from topography, cold air moves like honey and flows down slope at night).
Varieties: Onings has a list of "Latina" peonies that they grow in Italy in zone 9. These are mostly early blooming varieties. Choose early bloomers for best chance of success. This takes a little research.
Buy big: Get the biggest healthiest roots you can find. That means spending more money but imho wimpy roots won't make it here as our conditions are pretty extreme for peonies.
Planting: Don't bury the eyes. Many planting guides will tell you to put the eyes a few inches under the soil but that's for places that freeze hard. Our chill doesn't penetrate the soil so keep the eyes at the surface to grab any chill they can. Make sure to mulch them to protect from the summer heat.
So, if you keep all that in mind and want to give it a try please let me know how it goes! Consider it an experiment and give it five years before you decide. Then you too can join the Lunatic Gardening Fringe :)