While peonies are rather drought tolerant plants once established, it is important to give new peony transplants and 1 - 2 year old peony plants a good drink of water to keep them from drying out (frequency depends upon your soil and weather conditions). Older plants will benefit from an occasional watering, especially in the heat many of you are experiencing.
Now is the time to dead-head your peony plants, if you haven't done so already. Simply cut the dried-up flower head off of the stem, an inch or two below the flower head. It cleans up your plants for summer and helps tidy up your garden. Be sure to toss the spent petals and flower heads in the garbage, rather than composting them. This helps keep a healthier peony garden.
You can also let some of the peony flowers form seed pods, by not dead-heading. If a seed pod develops, it may produce viable seed. The seed pods generally start to crack open in late August, revealing their seeds. Peony seed pods can also be very beautiful. Not all varieties produce seed, but if they do, you can experiment with growing new plants from seed - perhaps gaining a new peony variety if the seed was cross pollinated.