The exterior wall adjoining one of our rooms gets a lot of sunlight in summer, and I suspect heats up the room a lot, as the exterior wall continues to radiate heat well after sunset during peak sunlight hours.
What kinds of materials could be used as a cladding (preferably decorative) to dissipate or disperse heat and cool down the adjoining room?
Since it's a "Heat in summer" problem, a traditional decorative and edible approach would be to train/trellis a plant or plants in front of the wall - grapes, vining tomatoes, espaliered fruit trees, perhaps even a fig depending on your climate - or purely decorative things like climbing roses, wisteria, or ivy - but ivy can be surprisingly aggressive, so research carefully.
This can be especially useful to grow things that might be a bit marginal in your climate and could stand some more warmth.
Put a false wall in front of the existing outside wall and allow air to flow between the two.
That will reduce the conducted heat into the room by a huge amount.
Trees ( maybe some other sorts of plants as well) near walls of buildings with sub surface basement, near terrasses, near concrete or plastered ways etc. can be a big problem in the long run, since the roots may destroy the sealing of a wall resulting in molded basements and health problems, and can lift and brake ways even made of concrete. The leaves or needles of high trees near buildings can clogg the tiles of roofs in a way that water can flow horizontally into the building. High trees can attract lightning. Plants near buildings can help burglars to be not seen by neighbours - and to get into upper floors.
As a rule of thumb, a distance of 15m should be to the next sub surface construction.
A photovoltaic screen protects the wall against heating up and can amortize in 6 to 20 years depending on sunshine duration, subsidiaries, own consumption, installation costs, feed in vs. feed out tariffs, maintenance costs. A PV system is a safe energy source during daytime in emergency situations or in locations with frequent power blackouts or shut downs.
As other answers noted, plants are good.
The other option is photovoltaic panels. You may reduce your electricity bill. Depending on your local electrical grid and code, you may even be able to get your bill negative (the power company to pay you something).
The cheap option is aluminium foil. It will reflect most of the sun energy back (and make the area near the wall even hotter). The professional solution is expanded or extruded polystyrene (EPS / XPS) insulation.
