Tons of structures in Tokyo are wooden. I lived in a steel-and-block place (which is apparently quite rare with most being steel-reinforced concrete), but all the apartments and single-family homes around me were wooden. Moreso when I moved further out of the city center.

I now live further north in Japan in a classically-designed wooden home and it’s still terrible in these temperatures (and we’re not nearly as hot as Tokyo up here).

I actually talked to an architect about this a couple of years ago and, though structures here are meant to breathe (mostly for airflow to avoid mold and later because of big problems with off-gassing and “sick house syndrome” when they tried to build more sealed structures with mechanical ventilation), they were not meant for the sustained hot conditions we face here today.