10 a.m. - If the heat gets to you, Ski Dubai in the Mall of the Emirates is one way to cool down and take some exercise, which can be a challenge in a land where hardly anyone goes for a walk and taking a taxi or a car is the standard way to go anywhere.

Another epitome of Dubai's embrace of the implausible, Ski Dubai boasts the world's first indoor black run (the most difficult grade of ski piste) and expends huge amounts of energy to ensure sub-zero temperatures keep the snow fresh.

12:30 p.m. - Head over to Bastakia for an insight into what Dubai was like before the boom. Heavily restored, but the closest Dubai has to genuinely old, Bastakia's traditional Arabic buildings have courtyards and wind towers -the earliest form of air conditioning - built to catch any breezes.

Before serious exploration, lunch options include the atmospheric Bastakia Nights, where menus are scrolls contained in ornate silver caskets, or the Local House Restaurant, which serves camel burgers and every other kind of camel meat.

3 p.m. - The surrounding area includes art galleries, the Grand Mosque, small museums and the Dubai Museum for a powerful sense of the revolutionary pace of change, triggered by the discovery of oil in the 1960s, after millennia of gentle evolution.

The museum is housed in the Al Fahidi Fort, completed in the 18th century when the city was under threat from tribal invasion. It fell into disrepair and has been completely restored.

Once inside (for a mere three dirhams), exhibits span the third millennium BC to the present day. They include ancient skeletons, depictions of Bedouin desert life and of the community of traders operating from tiny shops and traditional Arabic homes.

It's all a world away from the ultra modern malls and designer labels that dominate Dubai.

But the buzz of trade in the labyrinthine souks near to Dubai Museum symbolises deep continuity. Textiles, spices and wreathes of jasmine flowers are bargained for as they have been for centuries.

6 p.m. - Head back to some Dubai opulence with a drink/snack/dinner at the shamelessly opulent Burj Al-Arab, a self-styled seven star hotel.

Designed in the shape of a dhow's sail and set on its own private islet, reached by a private bridge, the Burj Al-Arab divides opinion. While many admire the exterior that has established it as a graceful Dubai landmark, some are appalled by its rococo interior, if they even manage to pass the barriers to entry.

Unless you're one of the guests paying thousands of dirham a night, you'll only be allowed in to inspect the giant aquariums and towering atrium with a bar reservation.

The Skyview Bar requires guests to spend a minimum of 225 dirhams on drinks/food as they gaze out on the skyline. There's also a smart casual dress code and the man in our party wearing flip-flops did not pass it.

Alternatively -- or if you have time for both before a late-night flight home -- take the monorail along Palm Jumeirah, one of Dubai's artificial islands formed in the shape of a giant palm.

As you travel along the trunk, you look out along palm fronds on which luxury housing is constructed and then at the very end, the Atlantis has for some outstripped the Burj Al-Arab as a statement hotel.

An enormous pink palace, with a huge key-hole arch-way, the Atlantis has it all: belly dancers, extraordinary glass sculptures and stone carvings, aquariums of rare fish, a water park, with exhilarating rides and specially cooled water, and a huge variety of bars and restaurants.

In July, it was chosen as the venue for one of the creditors' meetings of Dubai World, the massively indebted conglomerate that owns most of the emirate. The scores of bankers in attendance might have considered that this very, very grand asset is built on sand.