I suggest trying a clematis from the viticella group. A few that come to mind are: Etoile Violette, Polish Spirit, Blue Angel, Prince Charles and Emilia Plater (dark and light purple). I am in a colder climate than you, but I have read the Viticella clematis can take the heat!!

I have also read that viticella varieties are some of the most heat tolerant types. I came across this online photo the other day that shows the straight viticella species growing on an arch - it might give you an idea of whether you like this look. There are many viticella hybrids available in multiple colors with larger, more open faced flowers as well.

Here is a link that might be useful: photo of clematis viticella on arch

Here is an online article on the viticella type of clematis. Unfortunately, the link doesn't take you directly to the article. First click on the 4th tab on the top bar that says "Vines in the Garden". Under that will be displayed a list of articles - click on "Clematis Viticella Group". You might also be interested in another article in the list titled "Clematis in hot climates" and written by someone who grew clematis in Atlanta (hot and humid).

One of the first clematis I ever grew was the texensis hybrid "Duchess of Albany". I grew it in zone 8a in the Dallas, TX area in full, all day sun. It was surrounded by grass only so it didn't have to deal with reflected heat from a building or pavement. It did get some brown lower leaves, but it flowered very well, getting bigger every year. It's flowers face more upward, so it might not be as pretty for an overhead arbor. Hummingbird Farm's website says this about the texensis hybrids: "Give them a light, even gravelly, soil and full sun".

Here is a link that might be useful: article on clematis viticella

Thanks everyone for the great information and the links. I love the look of the clematis on the arbor. This information will help me to make a good choice.

Thanks to everyone for all of your input. I ordered 2 clematis from Brushwood. Both are of the viticella type as recommended. One is Madame Julia Correvon which has claret flowers. The other is Clematis Galore with dark purple flowers. I will plant one on each side of the branch arbor that I built, with the iceberg roses that are already there. I think they will fit in well with my cool color garden and the contrast with the white iceberg roses will be nice.