Generally speaking clematis in pots require a pot that is at least 18 X 18. However, whether such a pot will hold and be adequate for any clematis depends entirely on the clematis you plant in it. I have never heard of the clematis you mention so can offer no guidelines except to say try it and if the plant outgrows the pot, move it up as far as the pot size goes.

I just this morning dug up a clematis that had been in the ground 3 years. The root ball is about 20 inches across. I also wanted to put it into a large pot, however I am concerned about keeping the roots cool in the hot summer sun and also keeping it from freezing in the winter.

The roots need to be moist, not cool. Many people successfully grow Clematis in pots. They need to be large pots through. Wrapping with bubble wrap or Christmas lights helps during winter.

I was going to suggest the bubble wrap also BorS. Alternately, if you have a means of moving the pot housing the clematis, you can move it into an unheated garage which will keep the plant dormant but will also keep it from freezing solid.