Gran Vía cuts a long diagonal through central Madrid, northeast-southwest, and at lunch in July the north sidewalk — the one in the shadow of the Telefónica building and the Metropolis — sits a good five degrees cooler than the south. Everyone walks the south side anyway, because the shops are on the south side, and because the shaded sidewalk is where the city actually moves: scooters, deliveries, the kid running an errand. The trick is to commit to north and accept that you will cross to shop and cross back.
The picks below all pick the right side, then bail out into the smaller streets — Calle Reina, Calle Caballero de Gracia, the slot up to Chueca — where the four-story buildings throw block-long shadows by 1 PM. Stay Cool re-checks against the actual sun line; in late September these reverse and the south sidewalk wins. A useful caveat: the Schweppes sign on the Edificio Carrión is south-facing and the corner under it is in sun all day. Cross at Callao, not Red de San Luis.