Use the morning to get out and hike, either around town or at Lake Leatherwood or Beaver Lake. Get your shopping done early, or maybe take a horseback ride at one of the nearby stables.
Even as the day starts to heat up, Thorncrown Chapel is surrounded by tall shade trees. Enjoy one of the most uplifting places in the region, a chapel which has received acclaim for its architecture and its serenity.
In the broad heat of the day, take advantage of swimming and boating opportunities at Beaver Lake, Table Rock Lake, the Kings River, or Lake Leatherwood. The rivers usually run a little slower at this time of year, but you can always canoe below Beaver Dam, and the cold clear water will refresh your spirit.
If you don't want to get wet, but you'd still like to enjoy the water, try the tour of Beaver Lake on the Belle of the Ozarks. Even on the hottest days, you'll find a breeze on the lake.
If you just want to avoid the heat, use the afternoon to tour some galleries. Eureka Springs is home to a wonderfully varied and talented bunch of artists, and you can find some real bargains.
You can also take refuge from the sun with a spa treatment, or a cave tour. As the day stretches into evening, choose from the music shows or unwind at one of the watering holes around town. You have plenty of choices, so put the summer to work for you!