Please suggest some plants I should put at the base of the clems to keep their roots cooler.
The necessity to keep the roots of Clematis cool is an old myth. The rootball area has to be moist, not cool. Mulch it or use shallow rooted annuals.
Clems planted in close competition with other plants, especially tiny newly purchased Clems don't do well.
I have an average in-town lot with 31 clematis. I have a HUGE flower garden. The only thing I can say about planting below Clems, is to avoid deep rooted plants, they suck up too much of the water and entangle roots if you later want to transplant either. I use groundcover sedums, ALOT at the base of clems and roses. I also use heuchera to fill in under the leggy ones.