0.4. The highest average temperature in Bozeman is July at 71 degrees. The coldest average temperature in Bozeman is December at 20.3 degrees. The most monthly precipitation in Bozeman occurs in June with 2.6 inches.The Bozeman weather information is based on the average of the previous 3-7 years of data..4. The highest average temperature in Bozeman is July at 71 degrees. The coldest average temperature in Bozeman is December at 20.3 degrees. The most monthly precipitation in Bozeman occurs in June with 2.6 inches.