I was in Oklahoma with my daughter and was seduced by a lovely campanula in a nursery there. When I brought it home to central Texas, it died. Sorry, I don't know the variety.

I cannot think of any taller types which would do that well in dry heat....but there are many creeping camps (incurva, portenschlagiana, pocharskyana, pulla, isophylla, and even carpatica) which may well thrive in such conditions, although none of them are reknowned for being drought resistant.
You might try some of the adenophora and also wahlenbergia.
There is C.rigidipila, which is the southernmost campanula, growing in Ethiopia (but at altitude).

Ok.. Reading in PERENNIAL GARDENS FOR TEXAS by Julie Ryan, and she names C. poscharskyana and C. portenschlagiana as blooming ground covers, C. poscharskyana being the less heat tolerant of the two.

C. carpatica does well in the high plains. But sensitive to drought.

C. persicifolia is also mentioned. But peach.

OP again, recently i found at a local nursery three varieties of Campanula. Bought two, Campanula Blue Waterfall ( a low growing spreader), and Campanula Blue Peachbells (Peach leaved bellflower) which gets taller.
Anyone grow these here, especiallly in a hot climate?
Reviews on 'other' sites are from Alaska! And Ontario! The nursery gal said they will grow here as tender perreniels. I suspect the heat being the issue.

Full sun, but here?? I suspect east facing, west protection.

This is my thread to myself I guess! Bought some at lowes today. Blue clips campanula. Don't know much about it but the price was right!

Good luck. I saw some in Calloway's a couple of weeks ago, and they told me they would be blooming for about 2 more weeks, and wouldn't survive our hot summers. I'm in Houston. Let us know how yours do.