These may or may not appeal to you depending on your interests:
Get up really early and visit the Arizona Sonora Desert Museum about 15 miles west of the city, when it first opens and the outdoor animals are active in the cool morning.
Again early, visit Tohono Chul Park on the northwest side and have a bit to eat at their tea room afterwards.
Or if into hiking, again early, hike 1 mile on the Yetman Trail in Tucson Mountain park to the Old Stone House. Trailhead is just south of the west end of Speedway (where it turns into Gates Pass Road) on Camino de Oeste. Or any of the network of trails in Saguaro National Park east unit at the east end of Broadway or Speedway. Or drive the slow, scenic loop road in Saguaro east unit and do short hikes there (or skip the hiking if it's later in the day and hot). There's a fee to drive the loop road. Or visit Sabino Canyon and ride the tram, getting on and off to hike or just hang out under the cottonwood trees and enjoy the running creek.
Or if you want to be hiking in the cool, drive 1+ hour up the Catalina Highway to the top, or near the top, of Mt. Lemmon. If you go beyond the ski area to the very top it's only going to be about 73 degrees. Lots of great trails up high: Marshall Gulch south of Summerhaven near the top of the mountain or the control road, Lemmon Rock Lookout and the peak of Mt. Lemmon from the top, or the Aspen Trail around the east side of the ski runs. Slightly lower: Butterfly Trail, Box Camp Trail, Bear Wallow, and many more.
Down in the city there are several fine (air conditioned) museums including the Tucson Museum of Art downtown, the Arizona Historical Society on the west side of the University of Arizona campus, Arizona State Museum (anthropology) near Main Gate on the west side of campus, or the UA Museum of Art or the Center for Creative Photography on the NW side of campus. The Pima Air and Space Museum if you're into old airplanes.
Wander funky shops on Fourth Avenue just north of downtown. Ride the streetcar. Bicycle the Loop (google "tucson loop" . Visit some of the local breweries in the evening. Lots to do in Tucson! Enjoy!