0.7. The highest average temperature in Tucson is July at 87.3 degrees. The coldest average temperature in Tucson is December at 50.7 degrees. The most monthly precipitation in Tucson occurs in July with 4.6 inches. The Tucson weather information is based on the average of the previous 3-7 years of data.he Tucson, AZ air quality index is a median value which considers the most hazardous air pollutants. The Tucson, AZ air quality index is 18.3% less than the Arizona average and 7.5% less than the national average.