Brazilian here. They do. Although our shopping malls are cooled down with an air conditioning system. From my experience, the climate inside is often fresher but rarely too cold to need a jacket.
Also, sports have always been "unfair", not only because of differences in access to training but also because of "genetic anomalies". Back before Martin Luther King Jr., a lot of Americans would argue that Black athletes shouldn't compete among white athletes because of an "unfair advantage".
Don't American universities have dorms for the students?