By late October the afternoons in Diriyah are still hot, often in the thirties, but the evenings have changed. The air over Wadi Hanifah cools after sunset, the terraces along the valley fill, and Riyadh's season of being outdoors begins. Diriyah, on the north-western edge of the capital, is where much of that season is spent, by day in the lanes of a World Heritage site and at night at tables beside them, and both settings ask the same two things of a wardrobe: cover, and air.

At-Turaif, the historic district at the heart of Diriyah, was the seat of the first Saudi state, founded in the eighteenth century, and was inscribed as a UNESCO World Heritage Site in 2010. Its palaces and houses are built in the Najdi style, from sun-dried mud brick with thick walls, small openings and triangular vents cut high in the façades, an architecture shaped entirely by heat. The restored lanes are open to visitors, and the scale of the place, with Salwa Palace rising above the rest, suits a slow walk in the late afternoon, when the walls turn from beige to gold.

Saudi Arabia expects modest dress in public, and in a heritage site that expectation is visible; it is the starting point for what to wear in Diriyah. Visitors are asked to keep shoulders and knees covered, men as well as women; foreign women are not required to wear an abaya, but loose clothing that covers the arms and legs is the norm. Guidance evolves, so the site's current advice is worth reading before a visit. In practice this is linen's own ground. Long sleeves and long hems in a natural, absorbent cloth can feel cooler than bare skin in direct sun, and the crispness of the fibre keeps it from clinging.

For him, the afternoon in At-Turaif calls for a long-sleeved shirt and long trousers. The Bliss Linen Shirt in Sky Blue with PP Trousers 100% Linen in White is cool, correct and easy to walk in on packed earth and stone, and the sleeves can be turned back in the shade of a courtyard. In the evening, on Bujairi Terrace across the wadi, where restaurants look out over the lit ruins, a Laos Long Sleeve Linen Shirt in Dark Blue goes with PP Casual Linen Trousers in Black, the collar left open. A jacket is rarely needed before December.

Women have the same two needs. The PP linen blouse in Sky Blue with wide trousers covers what needs covering and keeps the air moving, and the HER Laos Linen Shirt in Grey over loose trousers is the quieter alternative for a long day on foot. A light scarf in the bag is always a sensible addition for a long evening out. Colour is welcome: the earth tones of the architecture are a good ground for a pale blue or a soft grey, and the evening crowd on the terraces is well dressed without being formal.

The setting rewards attention to the hour. Midday in the open lanes is hard work even in October, and the walls that look so soft in photographs radiate heat back by the early afternoon. The two hours before sunset are the time for At-Turaif; the hours after it are for the terraces, the gallery spaces and the restaurants, many of them with views back across the valley to the palaces. By ten the shirt put on at four will have softened at the elbows and the waist; on a terrace above the wadi that ease is part of its appeal.

Diriyah sits close to central Riyadh, and the wider wardrobe for what to wear in Riyadh follows the same principles of cover and air. Further north-west, the desert sites of AlUla ask for the same garments with a heavier layer for the cold nights. The months from October to March are the kingdom's outdoor season, and they are when a Gulf winter wardrobe in certified Belgian linen is worn most.

Diriyah's season runs into the spring, and the garments that serve At-Turaif in October serve it in March, with a heavier layer added for the cooler nights of midwinter.

Read more: What to Wear in Riyadh for Men  ·  What to Wear on Saudi Arabia's Red Sea