In Seattle facing west gets hot in summer...
1. will Al's mix work for this
2. what kind of tree? I thought about styrax or quince
3. how to keep the roots from getting to hot?
Are you adverse to a pine or juniper? Bougainvillea would love it, and bloom its head off for you - but needs a sunny indoor spot for the winter. Plumeria/Datura/brugs - not really trees, but tree-form plants with great blooms - indoors in winter.
Shade the pot or employ the pot-in-pot technique with outer pot being white and filling between the pots with a porous material (peastone/perlite .....) that you can wet each morning to take advantage of evaporative cooling. You could also use both (shading AND pot-in-pot), in case you can't or forget to wet the filler between the pots.