Let me throw in my own ideas since I come for a year-round hot country, and churches are not typically air-conditioned.
In my church (it’s a shrine, actually), there is an announcement said before every single Mass:
“We also humbly request that those wearing sleeveless clothing provide yourselves with shawls out of respect for the sacred Liturgy.”
At the door, the collection ladies keep some light shawls easily draped over a lady’s head, easily covering her shoulders and front. The shawl is well-cut and looks great on the ladies who wear them. If a lady comes in with a, er, textile shortage, the collectoras simply approach them discreetly, hand them a neatly folded shawl and invite them to put them on. No one is ever turned away, and most of the time, those approached are gracious about it.