Tucson early June temperatures average in the 90s. Sometime during the month, the temperature hits 100 degrees for the first time; but as they say it's a dry heat. In contrast to other cities where the heat index is always higher than the temp, it's LOWER here. Humidity averages less than 10%. Evenings are sublime; breezes sweep through the valley off the mountains that surround the city.
Because of our altitude (2500'+) it cools quickly at night. Depending on the timing of the winter rains, a few wildflowers may remain, but for sure, with or without rains, the cacti, along with mesquite and palo verde trees will be in bloom. You should bring along your favorite antihistamine to counteract unfamiliar and exotic pollens. It's important to keep hydrated, too.
Nevertheless, the hotel is comfortably refrigerated, and you can be oblivious to the temperature outside. Just stay inside!
Tucson is NOT like Phoenix. A friendly rivalry exists between the two. Phoenix is three times larger (3 million+), but Tucson is much older, with a rich history. It's cooler in Tucson, especially evenings, which rarely fall below 100 in Phoenix's summer. Phoenix is better for business, Tucson better for families. Both are often misspelled, however. We could go on...
Things to do in and around Tucson: