Actually many arch roof or "round roof" cars were built long before air conditioning became common. Some had mechanical forced air ventilation systems, others relied on roof vents to bring outside air into the car. Clerestory (not clear story) roofs had windows that opened and allowed air to escape, however, those windows were notoriosly "leakers". It was hard to seal all of those windows and keep them in good, tight fitting order. At best. the cars were often hot and stuffy in the summer but people didn't know any better until A/C. Most, or at least many, of those older clerestory roof cars had air conditioning added in the 1930's and 1940's and had all of their windows sealed. Often the A/C ducts were installed int the clerestory area of the ceiling or additional housing was added to the roof areas, alongside the clerestory roof to accomodate the A/C equipment.
Whether the cars were built with arch roofs or clerestories was a decision of the railroad itself. Part of that decision was costs, and I'm certain that the clerestory was more expensive to buld.
Paul Fischer