I am a graduate of Wellesley and still visit frequently. There are only three student apartments, I believe, and those are available to small groups of women who are choosing to live together, in a special lottery. In other words, you won’t just be assigned there as a transfer student. The dorms at Wellesley are not air-conditioned.
Have you visited Wellesley? The campus is stunning, and, yes, it is larger than Bryn Mawr, but its acreage includes a very large lake as well as a large golf course that most students don’t really think of as being part of campus. I’m not sure if it is as different as you think in that respect - having spent time at Bryn Mawr, I’d say they are similarly situated with a campus surrounded by a bustling suburban town.
Another campus surrounded by a suburban town is Agnes Scott College in Georgia. ASC has air conditioning in some of its dorms and advertises that it can offer special housing accommodations. Might be worth a phone call.
In the Northeast, however, you are right that air conditioning might be easier to find in larger universities with larger dorms.