Here is a list of heat-tolerant Clematis. You will have to check the zones.

Aotearoa
Gipsy Queen
Jackmanii Alba
Lady Betty Balfour
Serenata
Star of India
Victoria

Viticellas:
Abundance
Alba Luxurians
Betty Corning
Blue Belle
Etoile Violette
Kermensina
Madame Julie Correvon
Royal Velours
Sodertalje
Venosa Violacea

Side note: I got this list from the book Simply Clematis, by Edith Malek (president and founder of the American Clematis Society). I like this book because she worked, and still is working very hard at getting the zones, for all Clematis, correct for the US. I highly recommend the book - In addition to great photos, it has a lot of good information for beginners, but I think more experienced growers can appreciate it as well. If nothing else, it's great eye candy. I hope Edith doesn't mind that I posted one of her lists.

Janet,

Thank you so much for the list. I am familiar with some of the varieties you have listed and cannot wait to google the ones that I don't know.

Carolyn

I bought a Carnaby Clematis at Walmart's last week...haven't planted it yet..it has one little bloom...Carnaby's like shade? if so, that's great since most of my yard has shade...Can you name some other shade-loving Clematis? (Thanks)