Green roof, green walls for cooler house?

The west side of my house faces the summer sun all afternoon, and my house turns into a blast furnace every afternoon. We’ve put up one of those mesh 4-pole shelters over the porch in back, with wide roman blinds which can be lowered/rolled down, and it does at least keep the direct sun off the concrete , and off the screen door, but it doesn’t and can’t reach high up the wall.

I’ve heard that growing greenery on a roof lowers the temperature of the building. May I assume that growing greenery on exterior walls would also do the same? If so, what would be the best type of vines to grow, and more important, how would I best protect the exterior of my house while still growing the vines? I know those bloody things dig their tendrils into stone and damage it over time. And the siding of my house is wood.