Here is what I do in summer (or at least try to most of time) to keep my babies happy! I have adapted this things to-do list to accommodate gardeners in the other parts of the country as well. I have also written several articles that may help you cope with summer heat: Clematis: How to Beat the Summer Heat, Fogger Mist Nozzle and Gardening with Umbrellas.
Water! Make sure to regularly irrigate during the heat of summer. There is nothing worse than a thirsty clematis.
If leaves turn brown and it bothers you just cut them off!
To prevent the spread of stem rot (wilt), prepare a solution of horticultural disinfectant (1/4 teaspoon Physan 20 with 2 cups of water) in a spray bottle and use it to sanitize your clippers after each cut.
Re-mulch your garden beds if needed (see Too Much Mulch).
Keep an eye out for mildew. Spray with GreenCure every two weeks if mildew is a problem.
Fertilize your clematis doing a feeding your every 4 to 6 weeks. Alternate between GroPower Flower ‘n’ Bloom and GroPower All Purpose Plus.
Cut off seedheads (see Deadheading Your Clematis) if you want more blooms. Leave seedheads if you prefer the decorative whorls.
If your garden has been hit with snails as hard as mine has definitely continue to protect the clematis stems and flowers from snails and slugs. Spray with Pure ‘N’ Natural Snail & Slug AWAY and/or bait with a granular molluscicide such as Sluggo or That’s It.