A very good question and one that is difficult to answer. For one thing it depends upon where you live and also the type of soil you garden on.

Take the last three years in my garden. The last two years the summers have not been very hot, perhaps about three weeks that have been quite hot this year but the rest has been a mixture of warm, wet and cold winds. Three years ago was a long, hot summer

What I can tell you is the plants that have survived and flourished on my free draining sandy soil:
Crocosmia, Dahlias, Hardy Geraniums, Salvia, Hostas, Marjoram (both golden and green), Day Lilies, Eupatorium, Bamboo, Rosemary, Hebes, and Foxgloves. Roses have fared much better this year than they did in the very hot weather.

There are still many differing opinions as to how climate change will affect our gardens and the timescale for that change. My current garden is pretty full now with trees, shrubs and perennials. I know the mix will change along with the climate but I do not expect to rip out the lot overnight and replace them with plants from desert regions. It will be a gradual change over many years and the good news is many governments are now taking note of what the scientists have been warning us about for quite some time.

At the moment I would advise you to plant whatever flourishes at the moment in you location. Check what is selling at your local garden centre or nursery and take note of what is growing well in your neighbourhood or even make visit to any large gardens open to the public in your area.

Rodger