Plants for Dry soil and for Wet Soil
When the weather turns very hot and very dry in summer gardeners tend to panic as lawns turn brown and plants shrivel. Many gardeners feel the need to water their plants daily, but really there is no need. It might be better to replan your borders to include plants that can cope with drought, and flooding. In over 40 years has it not rained at some point during autumn and winter. There may have been dry periods over winter, but it will rain.
However, apart from choosing plants that cope with drought and flooding, there are a various things that can be done to help you garden stay reasonably green during excessively hot periods.
1. Don't tidy borders. Although it is tempting to cut back old flower stems when they look untidy, leaves provide shelter for insects and other small creatures like frogs and prevent the soil from loosing even more water through evaporation. If you look at the grass under trees you will see that, while grass in open areas is brown, much of the grass under the shade of trees remains green.
2. When choosing new plants think about what your soil is like in summer as winter, as well as the type of soil you have in the garden. Soil can also vary in different parts of the garden. It may be damp against a north wall because it does not get the sun and so won't dry out, but 2 metres from the wall, where the sunshines, the soil may dry out.
3. As the UK varies by region what will grow in south eastern England may not grow in north west Scotland, so look at gardens in your region so see what thrives.
What thrives in my garden when temperatures rise.
As you say Intersectional peonies have done brilliantly, probably due to the thickness of the leaves which they inherit from Woody (tree) peonies. Woody peonies come from hotter areas of China than rbaceous peonies, which tend to die back by the end of August.
All perennials are fine in drought and wet soils, but some are burnt off in extreme heat. Plants like Persicaria are great but are better grown in shadier spots.
Here is a shortish list perennials that have done well in the new border and do well in our wet soil over winter:
Achillea but only 'Moonshine' has proved to be perennial in wet winters
Aconitum
Amsonia
Aruncus
Asters - the ones with shiny leaves have done better in drought conditions such as 'Glow in the Dark'
Baptisia
Brunnera - particularly the silver-leaved types
Centranthus
Cirsium
Echinops
Eryngium
Helenium
Irises: Bearded irises are fine in wet conditions as long as they don't sit in water-logged soil
Nepeta
Origanum
Phlomis russelliana
Salvia but only Salvia glutinosa and Salvia verticilata types do well in wetter soils
Sanguisorba all types suprisingly
Sedum
Selinium
Stachys byzantina and it's types
Verbena