I saw your picture in the other post and all I can suggest is a huge pot to keep the soil cool. Say, 24 inches deep.

Great, the pot will definitely be that deep. Thanks!!!

The roots don't need to be cool, but they do need to have even moisture without being soggy, so your biggest concern will be keeping them from getting too dry. I don't know where you are and what your weather is like. Regardless, you'll need to check moisture morning and evening once the plants get large until you have a feel for how quickly the pots dry out.

Have you considered planting one in the ground to grow up your fence?

I have mine in western late afternoon sun in California, zone 9b- 85-100 all summer.They are fine as long as there is a lovely pile of compost to keep the roots cool- I had out two inches and had to water every day, then I added 3 more inches (total 5 inches) and now can water 2x a week and they are green and happy.
Pea

Thanks everyone!! Yes I am actually thinking instead of doing the pots right there, we are going to be moving the fence back and I am thinking on putting them along the fence in the back instead of right there by the house. I can't seem to find anywhere local that sell Clematis until Spring so I will probably end up waiting until then :-) Unless I can get Joys etc to ship me some in the Fall when things start shipping again.