Better cool than hot. Wendy Teague has worked as a server in restaurants and her firm has designed restaurants, so she's familiar with their guts. Also, entryways tend to be more formal in regions where the weather requires overcoats. You see a lot more revolving doors. In the Bay Area you most often push or pull open the glass front door and then hover over other diners' tables.
Square footage being at a premium is only one reason.
Another is that a restaurant usually takes over an existing retail space. And the previous tenant probably had no need for an expensive heating, ventilating and air-conditioning system that could be finely regulated to keep one area cool and another warm. If it's hot in the kitchen, and it's always hot in the kitchen, the cook may get cranky. Meanwhile, the front staff runs around a lot. All we diners warm is our chairs.