Madrid is higher altitude and much drier and dustier than one would think. If sand inhilation bothers you keep water with you at all times and even something like an aspirator if you need one. Also, the sun seems to be much stronger and brighter to many people (still haven't been able to figure this one out) so you might want to keep sunglasses with you too!

A broad-brimmed hat or cap! Carry around a 2 liter bottle of water, and imbibe liberally and often. Sunstroke ("glope del sol") is serious here. Stay in the shade as much as possible. You will gain a new understanding why everything closes down from 2 until 4pm! Oh, and sunscreen, lots of sunscreen!

...and keep your eyes open, camels run fast..